LOW-POWER SOURCE OF SQUEEZED LIGHT
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`tnventor:
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`Bonnie L. Schmittberger
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`BACKGROUND
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`Field
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`[0001]
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`The present disclosure generally relates to squeezed light apparatuses and systems,
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`for example, low-power squeezed light sources.
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`Background
`
`(6002)
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`In quantum physics, an oscillating physical quantity (e.g., a light wave) cannot have
`
`precisely defined values at all phases of the oscillation. Squeezed light is a type of non-
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`classical light in which one ofits field quadratures has a reduced or “squeezed” noise at the
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`expense of added noise in the other quadrature. Squeezed light can have a quantum noise
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`reduction belowa shot noise level, which has applications in precision optical measurements
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`and quantum communication. Shot noise is the noise level
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`that would be measured by
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`coherent light of the same optical power when using the same detection scheme. Current
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`techniques to generate quadrature-squeezed light require various optical components and
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`high input powers and, thus, are impractical for scaling to a low-power and portable device.
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`SUMMARY
`
`{0003}
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`Accordingly, there is a need to provide a low-power and portable squeezed light
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`source with a reduced size, weight, and power (SWaP) to improve the precision ofoptical
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`measurements and implement continuous-variable quantum cornmunication protocols. To
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`meet this need using degenerate four-wave mixing (DFWM), excess noise must be reduced.
`
`(0004
`
`in some embodiments, a degenerate four-wave mixing (DFWM) squeezed light
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`apparatus includes one or more pump bearns, a probe beam, a vaporcell, a repurmp bearn, and
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`a balanced differential detector or a joint homodyne detector.The one or more pump beams
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`includes an input power of no greater than about 150 mW. The probe beam is configured to
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`overlap the one or more pump beams. The vapor celf includes an atomic vapor, a first
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`window, and a second window. The atomic vapor is configured to interact with the
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`overlapped pump and probe beams to generate an amplified probe beam and a conjugate
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`beam. The repump beam is configured to optically purnp the atornic vapor to a groundstate
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`and decrease atomic decoherence of the atomic vapor. The balanced differential detector or
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`the joint homodyne detector is configured to measure squeezing due to quantumcorrelations
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`between the amplified probe beam and the conjugate beam. The one or more pump beams,
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`the probe bearn, and the repump beam are configured to reduce spontaneous emission of the
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`atomic vapor and generate two-mode squeezed light by DFWMin the atomic vapor with
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`squeezing of at least 3 dB below shot noise.
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`{0003}
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`In some embodiments, the input power of the one or more pump beams is no greater
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`than about S50 mW. In some embodiments, the input power of the one or more pump beams is
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`no greater than about 20 mW.
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`10006]
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`In some embodiments, the repump beam is cylindrical. In some embodiments, the
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`repump bear is an annulus. In some embodiments, the repump beam includes two counter-
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`propagating annular repump beams. In some embodiments, an input power of the repump
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`beam is no greater than about the input power of the one or more pump beams.
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`{6607}
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`In some embodiments, the one or more pump beams, the probe bearn, and the vapor
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`cell are arranged in a forward-scattering geometry. In some embodiments, the one or more
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`pumip beams, the probe beam, and the vapor cell are arranged in a backward-scattering
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`geometry.
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`[6008]
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`In sorne embodiments, the two-mode DFWMsqueezed light includes squeezing ofat
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`least 6 dB below shot noise.
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`In some embodiments,
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`the balanced differential detector
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`includes an intensity-difference detector. In some embodiments, the joint homodyne detector
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`includes a pair of homodyne detectors.
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`{0009}
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`In some embodiments, the first and second windows have a ternperature greater than
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`an exterior surface of a cylindrical wall of the vapor cell.
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`In some embodiments, a
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`temperature of the vapor cell is about 30 °C to about 100 °C. In some embodiments, the
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`temperature is about 35 °C to about 45 °C. In some embodiments, a longitudinal length of the
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`vaporcell is about 0.5 cm to about 10 cm. In some embodiments, the atomic vapor includes a
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`rubidium vapor.
`
`[0016]
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`In some embodiments, theDFWMsqueezed light apparatus includes a portable diode
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`laser. In some embodiments, the portable diode laser includes a volume of no greater than
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`about 100 cm’. In some embodiments, the portable diode laser includes an output power of
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`no greater than about 150 mW. In some embodiments, the DFWMsqueezed light apparatus
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`includes a portable integrated photonic chip.
`
`{0011}
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`In some embodiments, a method of forming a low-power squeezed light source
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`includes overlapping one or more pump beams and a probe beam. The one or more pump
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`beams includes an input power of no greater than about 150 mW. In some embodiments, the
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`method further includes interacting an atomic vapor with the overlapped pump and probe
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`beams to generate an amplified probe beam and a conjugate beam. In some embodiments, the
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`method further includes optically pumping the atomic vapor with a repump beam configured
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`to decrease atomic decoherence of the atomic vapor. In some embodiments, the method
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`further includes generating two-mode squeezed light by degenerate four-wave muxing
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`(DFWM) in the atomic vapor with squeezing of at least 3 dB below shotnoise.
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`{0012]
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`In some embodiments, the overlapping includes applying an input powerof the one or
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`more pump beams no greater than about 50 mW. In some embodiments, the optical pumping
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`includes an annular repump beam. In some embodiments, the two-mode DFWMsqueezed
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`light includes squeezing of at least 6 dB belowshot noise. In some embodiments, the method
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`further includes measuring an intensity-difference squeezing due to quantum correlations
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`between the amplified probe beam and the conjugate beam with a balanced differential
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`detector. In some embodiments, the method further includes measuring quadrature squeezing
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`due to quantum correlations between the amplified probe beam and the conjugate beam with
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`a joint homodyne detector.
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`10013]
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`Further features and exemplary aspects of the ernbodiments, as well as the structure
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`and operation of various embodiments, are described in detail below with reference to the
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`accompanying drawings. It is noted that the embodiments are not limited to the specific
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`embodiments described herein. Such embodiments are presented herein for illustrative
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`purposes only. Additional embodiments will be apparent to persons skilled in the relevant
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`art(s) based on the teachings contained herein.
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`BRIEF DESCRIPTION OF THE DRAWINGS
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`{O014]
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`The accompanying drawings, which are incorporated herein and form a part ofthe
`
`specification, illustrate the embodiments and, together with the description, further serve to
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`explain the principles of the embodiments and to enable a person skilled in the relevant art(s}
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`to make and use the embodiments.
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`[0015]
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`FIG.
`
`1
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`is a schematic illustration of a squeezed light wave, according to some
`
`embodiments.
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`{0016}
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`iG. 2 is a schematic tlustration of an energy diagram for degenerate four-wave
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`mixing (OFWM)in a two-level atomic system, according to some embodiments.
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`{0017]
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`FIG. 3 is a schematic illustration of a backward-scattering geometry, according to
`
`some embodiments.
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`iG013]
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`FIG. 418 a schematic illustration of a forward-scattering geometry, according to some
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`embodiments.
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`{6019}
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`FIG. 5 is a schematic perspective illustration of a DFWMsqueezed light apparatus,
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`according to some embodiments,
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`10026]
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`FIG. 6 is a schematic illustration of a joint homodyne detector, according to sorne
`
`embodiments.
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`{0021}
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`FIG. 7 is a schematic perspective illustration of the repump beam of the DFWM
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`squeezed light apparatus of FIG. 5, according to some embodiments.
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`10022]
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`FIG. 7A is a schematic partial cross-sectional illustration of the repump beam of FIG.
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`7, according to some embodiments.
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`{0023}
`
`[6024]
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`FIG. 8 is a schematic illustration of a plot of noise, according to some embodiments.
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`FIG. 9 is a schematic perspective illustration of a DFWMsqueezed light system,
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`according to some embodiments,
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`10025]
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`FIG. 10 is a schematic cross-sectional
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`illustration of the DFWM squeezed light
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`system of FIG. 9, according to some embodiments.
`
`{0026}
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`FIG.
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`11 is a schematic illustration of a plot of squeezing, according to some
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`embodiments.
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`10027]
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`FIG. 12 illustrates a flow diagram for forming a low-power squeezed light source,
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`according to some embodiments.
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`{00238}
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`The features and exemplary aspects of the embodiments will become more apparent
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`from the detailed description set forth below when taken in conjunction with the drawings, in
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`which like reference characters identify corresponding elements throughout. In the drawings,
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`like reference numbers generally indicate identical, functionally similar, and/or structurally
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`similar elements. Additionally, generally,
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`the left-most digit(s) of a reference number
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`identifies the drawing in which the reference number first appears. Unless otherwise
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`indicated, the drawings provided throughout the disclosure should not be interpreted as to-
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`scale drawings.
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`DETAILED DESCRIPTION
`
`[0029]
`
`The
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`embodiment(s) described,
`29
`Ee
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`and
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`references
`
`in
`
`the
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`specification to
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`“one
`
`embodiment,”
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`“an embodiment,” “an example embodiment,” “some embodiments,” etc.,
`
`os
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`indicate that the embodiment(s) described may include a particular feature, structure, and/or
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`characteristic, but every embodiment may not necessarily include the particular feature,
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`structure, and/or characteristic. Moreover, such phrases are not necessarily referring to the
`
`same embodiment. Further, when a particular feature, structure, and/or characteristic is
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`described in connection with an embodiment, it is understood that itis within the knowledge
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`of one skilled in the art(s) to effect such feature, structure, and/or characteristic in connection
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`with other embodiments whether or not explicitly described. The scope of this disclosure is
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`not limited to the disclosed embodiment(s) but is instead defined by the claims appended
`
`hereto.
`
`[0036]
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`Spatially relative terms,
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`such as “beneath,” “below,” “lower,” “above,” “on,”
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`“upper,” and the like, may be used herein for ease of description to describe one element or
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`feature’s relationship to another elemeni(s} or feature(s) as illustrated in the figures. The
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`spatially relative terms are intended to encompass different orientations ofthe device in use
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`or in operation in addition to the orientation depicted in the figures. The apparatus may be
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`otherwise oriented (rotated 90 degrees or at other orientations) and the spatially relative
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`descriptors used herein maylikewise be interpreted accordingly.
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`[0031]
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`The term “about” or “substantially” or “approximately” as used herein indicates the
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`value of a given quantity that can vary based on a particular technology. Based on the
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`particular technology, the term “about” or “substantially” or “approximately” can indicate a
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`value of a given quantity that varies within, for example, 1-15% of the value (e.g., +1%,
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`42%, 5%, +10%, or +15%of the vaiue).
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`[0032]
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`Embodiments ofthe disclosure may be implemented in hardware, firmware, software,
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`or any combination thereof. Embodiments of the disclosure may also be implemented as
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`instructions stored on a machine-readable medium, which maybe read and executed by one
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`or rnore processors. A machine-readable medium may include any mechanism for storing or
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`transmitting information in a form readable by a machine {e.g., a computing device). For
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`example, a machine-readable medium may include read only memory (ROM), random
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`access memory (RAM), magnetic disk storage media, optical storage media, flash memory
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`devices, and/or electrical, optical, acoustic, or other forms of propagated signals (e.g., carrier
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`waves,
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`infrared signals, digital
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`signals, etc.), and others. Further,
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`firmware, software,
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`routines, and/or instructions may be described herein as performing certain actions. However,
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`it should be appreciated that such descriptions are merely for convenience and that such
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`actions in fact result from computing devices, processors, controllers, and/or other devices
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`executing the firmware, software, routines, instructions, etc.
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`[0033]
`
`[0034]
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`Exemplary DFWMSqueezed Light Apparatuses
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`As discussed above, an oscillating physical quantity (e.g., a ight wave) cannot have
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`precisely defined values at all phases of the oscillation. Under the Heisenberg uncertainty
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`principle, quantum uncertainty exists for certain pairs of physical properties, for example, a
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`light wave’s quadratures of the electric field, phase and amplitude. Quantum uncertaintyis
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`visible when identical measurements of the same quantity (e.g., observable) on identical
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`objects (e.g., modes of light) give different results (e.g., eigenvalues). A squeezed state is a
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`quantum state described by two non-commuting observables having a continuous spectra of
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`eigenvalues. A quadrature-squeezed state of light is characterized by noise whose standard
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`deviation in one quadrature is belowthat of coherent light of the same optical power.
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`[0035]
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`Squeezed light is a type of non-classical light in which one of its field quadratures
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`(e.g., amplitude or phase} has a reduced (squeezed”) noise at the expense of added noise in
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`the other quadrature. Squeezed light has a reduced quantum uncertainty while anti-squeezed
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`light has a larger quantum uncertainty. Diminishing the quantum noise at a specific
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`quadrature (e.g., phase) of a light wave increases the noise of the complementary quadrature
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`(e.g., amplitude).
`
`[0036]
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`FIG.
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`|
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`illustrates
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`squeezed light wave 100, according to various exemplary
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`embodiments. Squeezed light wave 100 can include an oscillating electric field 102 with a
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`first quadrature (e.g., phase 103) and a second quadrature (e.g., amplitude 105). As shown in
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`fomi
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`FIG. 1, oscillating electric field 102 can include an anti-squeezed or increased amplitude
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`uncertainty 106 and a squeezed or reduced phase uncertainty 104 (e.g, phase-squeezed
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`light). Reduced phase uncertainty 104 can have a reduced quantum noise compared to the
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`phase noise of a coherent field of the same optical power (e.g., shot noise).
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`In some
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`embodiments, oscillating electric field 102 can include an antt-squeezed or increased phase
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`uncertainty and a squeezed or reduced amplitude uncertainty (e.¢., amplitude-squeezedlight).
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`[0037]
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`Two-mode squeezing involves two modes ofthe electric field which exhibit quantum
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`noise reduction below the shot noise level in a linear combination of the quadratures of the
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`fields. Shot noise is the noise level that would be measured by coherent light of the same
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`optical power when using the same detection scheme. Two-mode squeezing can be exploited
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`to generate continuous-variable entanglement. Squeezed light can be generated using
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`nonlinear optical processes (e.g., non-degenerate four-wave mixing, parametric down-
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`conversion). However,
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`these techniques require various optical components, high input
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`powers (e.g., greater than 500 mW), have low power conversion efficiencies (e.g., less than
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`0.1%), and are not currently compact (e.g., not easily portable). Thus, current techniques are
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`impractical for scaling to a low-powerand portable squeezed light source.
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`10033]
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`Four-wave mixing is a nonlinear interaction between light and matter that permits the
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`transfer of energy among four modes of the electric field via their interaction with a
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`nonlinear medium (e.g., an atomic vapor). Compared to non-degenerate nonlinear optical
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`processes, degenerate four-wave mixing (DFWM) can generate squeezed light via a
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`nonlinear optical process that requires fewer optical components and has a high power
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`conversion efficiency (e.g., greater than 10%) at low input pump beam powers (e.g., less than
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`150mW). For example, in rubidium (Rb), the 5S:to 5P32 atomic transition (e.g., 780.2 nm)
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`is easily accessible with a simple diode laser system.
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`[0039]
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`In atomic physics, fine structure describes the splitting of spectral lines due to the
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`coupling between the orbital and spin angular momenta of the valence electron. For the 5812
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`ground state of Rb, this total momentum, defined in units of Planck’s constant hbar (fh), is
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`designated by the subscript 1/2. The hyperfine structure describes additional splitting of the
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`fine structure spectral lines due to the coupling of the valence electron’s momentum to the
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`nuclear angular rormentum. The hyperfine energy state is designated by the parameter FP’.
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`Doppler broadening of spectral lines is a result of thermal motion of an atomic vapor at a
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`finite termperature relative to an opticalfield.
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`10046]
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`For example, electrons in Rb atoms are found in the ground state, 5Sio, and upon
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`excitation are moved to a higher energy state depending on the discrete energy received. The
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`5$i2 to 5P32 atomic transition can be approximated as a two-level atomic system with a
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`ground state (e.g, * = 3) and a Doppler-broadened excited state. Atoms whose electron has
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`decayed into the other hyperfine ground state can be treated as decohered atoms. Decohered
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`atoms must be opticaily pumped back into the ground state (e.g., F = 3) before they can
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`participate in the DFWMprocess.
`
`(0041
`
`FiG. 2 illustrates energy diagram 200 for DFWM, according to various exemplary
`
`embodiments. Energy diagram 200 can include a ground state 210 (e.g, SSin, F = 3), a
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`Doppler-broadened excited state 220 (e.g., 5P32), and a virtual excited state 230 separated by
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`a trequency detuning (A) 240 from Doppler-broadenedexcited state 220. Optical fields (e.g.,
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`pump beam(s) 202, probe beam 206) are frequency tuned to a frequency that is greater than
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`the resonant ground-to-excited state 215 transition frequency by frequency detuning (A) 240.
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`Resonant excitation (eg, A = 0) causes nearly all optical fields to be absorbed and
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`spontaneously reemitted and, thus, squeezing cannot occur when frequency detuning (A} 240
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`is zero (e.g., A = 0) or close to zero (e.g., A ~ 0). In some embodiments, frequency detuning
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`(A) 240 can be at the edge of or just outside Doppler-broadened excited state 220. For
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`example, frequency detuning (A) 240 can be about 300 MHz to about 800 GHz.
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`10042]
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`As shown in FIG. 2, energy diagram 200 can approximate a two-level atomic system
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`with pump beam(s) 202 driving atomic transitions between ground state 210 and virtual
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`excited state 230 to amplify probe beam 206 and produce conjugate beam 208. Pump
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`beani(s) 202 can drive first and second atomic transitions in an atomic vapor(e.g., Rb atoms)
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`from ground state 210 to virtual excited state 230. In the first transition, pump beam 202
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`excites an atom (e.g., Rb atom) in the atomic vapor from ground state 210 to virtual excited
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`state 230, and probe beam 206 induces stimulated emission from virtual excited state 230 to
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`ground state 210. This excitation-emission process changes the dipole moment of the atomic
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`vapor. In the second transition, pump beam 202 excites atoms (e.g., Rb atoms) in the atomic
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`vapor with the new atomic dipole moment and incudes emission that produces conjugate
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`beam 208. The interaction of pump bear 202 with the dipole moment inducedin the atoms
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`9.
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`by the second transition then, in a synergistic manner, amplifies probe beam 206 ofthe first
`transition. In some embodiments, ground state 210 can be / = 3 for a “Rb vapor and/or F = 2
`for a *’Rb vapor. For example, as shown in FIG. 2, ground state 210 can be F =3 for a SRb
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`vapor,
`
`{0043}
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`DFWMcan utilize a two-level atomic system in which all beams have the same
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`frequency. DF WM can occur even if only two beams interact (e.g., pump beam and probe
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`beam). The pump and probe beams have the same frequency but different wavevectors (e.g.,
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`k-vectors) since they must propagate at a small angie relative to one another in order to
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`conserve momentum in the DFWMprocess. The sum of the é-vectors of the pump beams
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`must equal the sum of the &-vectors of the probe and conjugate beams.
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`[0044]
`
`In a backward-scattering DFWM geometry, two counter-propagating pump beams
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`and a probe beam propagating at a small angle (e.g., small angle 305) relative to one of the
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`punip beams overlap inside a nonlinear medium(e.g, an atomic vapor) and a conjugate beam
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`is generated via a four-wave mixing mechanism. The forward pump beam and the probe
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`beam propagate in one direction (e.¢., forward) and the backward pump beam propagates in
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`the opposite direction (e.g., backward). Thus, the conjugate beam (¢.g., fourth beam) also
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`comes out in the opposite direction (e.2., backward). The conjugate beam is a wavevector
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`reversed replica of the probe beam(e.g, its phase is conjugate to that of the probe beam) and
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`any classical noise present on the input probe beam will be canceled out uponjoint detection.
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`Any sources of excess noise that arise after the nonlinear processes (e.g.,
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`that occur
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`independently} on one or both beams will not be canceled out.
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`10045]
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`FIG. 3 illustrates backward-scattering geometry 300, according to various exernplary
`
`embodiments. Backward-scattering geometry 300 can include pump beams 302 and probe
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`beam 304 impingent upon a vapor cell 310. Vapor cell 310 can include an atomic vapor 311
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`(e.g., Rb) enclosed within a container 312 extending a length 314. As shown in FIG. 3, the
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`interaction of pump beams 302, probe beam 304, and atomic vapor 311 creates (e.g., via
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`DFWM) amplified probe beam 306 and conjugate beam 308. Amplified probe bearn 306 and
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`conjugate beam 308 can be a squeezed light source, for example, two-mode squeezed light
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`by DFWMwith squeezing of at least 3 dB below shot noise. As shown in FIG. 3, pump
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`beams 302 and probe bear 304 can propagate at small angie 305.
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`In some embodiments,
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`small angle 305 can be about 1 degree to about 10 degrees. For example, small angle 305 can
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`be about 5 degrees. In some embodiments, backward-scattering geometry 300 can be utilized
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`in DFWMsqueezed light apparatus 500 and/or DFWMsqueezed light system 900.
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`10046]
`
`in a forward-scattering DF'WMgeometry, all input beams propagate in one direction
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`(e.g., forward) and, thus, the conjugate bear (e.g., fourth beam) also propagates in the same
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`direction (e.g., forward). All input beams can be focused and mixed using, for example, a
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`single lens, which can create a high photon density and efficient wave mixing.
`
`{6047}
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`FIG. 4 illustrates forward-scattering geometry 400, according to various exemplary
`
`embodiments. Forward-scattering geometry 400 can include pump beam 402 and probe beam
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`404 impingent upon a vapor cell 410. Vapor cell 410 can include an atomic vapor 411 (e.g,
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`Rb) enclosed within a container 412 extending a leneth 414. As shown in FIG. 4,
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`the
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`interaction of pump beam 402, probe beam 404, and atornic vapor 411 creates (e.2., via
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`DFWM) amplified probe beam 406 and conjugate beam 408. Amplified probe beam 406 and
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`conjugate beam 408 can be a squeezed light source, for example, two-mode squeezed light
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`by DFWMwith squeezing ofat least 3 dB below shot noise. As shown in FIG. 4, pump and
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`probe beams 402, 404 can propagate at small angle 405. In some embodiments, small angle
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`405 can be about 0.01 degrees to about | degree. For example, small angle 405 canbe about
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`O.5 degrees. In some embodiments, forward-scattering geometry 400 can be utilized in
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`DFWM squeezed light apparatus 500 and/or DFWM squeezed light system 900. For
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`example, as shown in FIG. 5,DFWMsqueezed light apparatus 500 can utilize a forward-
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`scattering geometry similar to forward-scattering geometry 400 shown in FIG.4.
`
`[0048]
`
`FIGS. 5-7 illustrate DFWM squeezed light apparatus 500, according to various
`
`exemplary embodiments. DFWMsqueezed light apparatuses and systems as discussed below
`
`can reduce excess noise and provide a low-power and portable squeezed light source with a
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`reduced size, weight, and power (SWaP) to improve the precision of optical measurements
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`and/or enable continuous-variable quantum communication protocols.
`
`10049]
`
`FIG.
`
`5
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`illustrates DFWM squeezed light apparatus 500, according to various
`
`exemplary embodiments. DFWMsqueezed light apparatus 500 can be configured to generate
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`squeezed light with an input power of no greater than about 150 mW. DFWMsqueezed light
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`apparatus 500 can be configured to generate two-mode squeezed light by DFWMwith
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`squeezing of at least 3 dB belowshot noise. Although DFWMsqueezed light apparatus 500
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`is shown in FIG. 5 as a stand-alone apparatus and/or system,
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`the embodiments of this
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`disclosure can be used with other optical systems, such as, but not limited to, a portable diode
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`laser, a portable integrated photonic chip, DFWM squeezed light system 900, and/or other
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`-li-
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`optical systems.
`
`[0050]
`
`DFWMsqueezed light apparatus 500 can include pump beam 502, probe beam 504,
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`amplified probe beam 506, conjugate beam 508, vapor cell 510, heating system 520,
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`temperature sensing system 530, processor 540, optical block 542, balanced differential
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`detector 550, and/or repump beam 590. Similar to forward-scattering geometry 400 shown in
`
`FIG. 4, pump beam 502 and probe bearn 504 can propagate at a small angle 505 and overlap
`
`in vapor cell 510 to generate amplified probe beam 506 and conjugate beam 508 by DFWM.
`
`Pump beam 502, probe beam 504, and vapor cell 510 can be configured to generate two-
`
`mode squeezed light (e.2., amplified probe beam 506 and conjugate beam 508) by DFWM,
`
`for example, with squeezing of at
`
`least 3 dB below shot noise. In some embodiments,
`
`DFWMsqueezed light apparatus 500 can generate two-mode squeezed light by DFWMwith
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`squeezing ofat least 6 dB below shot noise. In some embodiments, DFWMsqueezed light
`
`apparatus 500 can generate single-mode squeezed light by DFWM. In some embodiments,
`
`pump beam 502, probe beam 506, and/or repump beam 590 can be produced by an optical
`
`source (not shown). For example, as shown in FIG. 10, optical source 932 can be a compact
`
`coherent light source (e.g., diode laser, DFB laser, etc.) configured to produce pump beam
`
`502, probe beam 506, and/or repump beam 590.
`
`[6051]
`
`Pump beam 502 can be configured to excite an atomic vapor 511 in vapor cell $10,
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`for example, from a ground state (e.g., ground state 210, e.g., 5512, shown in FIG. 2) to an
`
`excited state (e.g., virtual excited state 230 shown in FIG. 2). Pump beam 502 can include an
`
`input power of no greater than about 150 mW. In some embodiments, the input power of
`
`pump beam 502 can be no greater than about 50 mW. In some embodiments, the input power
`
`of pump beam 502 can be no greater than about 20 mW. For example, pump beam 502 can
`
`be produced by a low-powerportable diode laser and/or a distributed feedback COFB)laser.
`
`In some ernbodiments, pump bearn 502 can be produced by a pump source (not shown). For
`
`example, as shown in FIG. 10, optical source 932 can be a compact coherent light source
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`(e.g., diode laser, DFB laser, etc.) configured to produce pump beam 502.
`
`In some
`
`embodiments, pump beam 502 can be polarized (e.g., linearly, circularly, etc.). For example,
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`pump and probe beams 502, 504 can be cross-polanzed {e.g., orthogonal).
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`In some
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`embodiments, pump beam 502 can include a wavelength in the visible, near-infrared, and/or
`
`infrared. For example,
`
`the wavelength of purnp beam 502 can be about 780.2 nm, for
`
`example, when atomic vapor 511 comprises Rb.
`
`[0052]
`
`Probe beam 504 can be configured to overlap pump beam 502 inside vapor cell 510
`
`such that pump beam 502, probe beam 504, and atomic vapor 511 can undergo DFWM.
`
`Probe bear 504 can include an input power of no greater than about 15 mW{e.¢., an order
`
`of magnitude lower than pump beam 502). In some embodiments, the input power of probe
`
`beam 504 is about 1 pWto about 0.5 mW. For example, probe beam 504 can be about 100
`
`uW. In some embodiments, probe beam 504 can include a portion of pump beam 502. For
`
`example, a portion of pump beam 502 can be siphoned off via a beamsplitter (e.g¢., 99:1) to
`
`form separate probe beam 504. In sorne embodiments, probe bear 504 can be producedbya
`
`probe source (not shown) and/or a pump source (not shown). For example, as shown tn FIG.
`
`10, optical source 932 can be a compact coherent light source (e.g., diode laser, DFB laser,
`
`etc.) configured to produce probe beam 504. In some embodiments, probe beam 504 can be
`
`polarized (e.g., linearly, circularly, etc.). For example, pump and probe beams 502, 504 can
`
`be cross-polarized (e.g., orthogonal). In some embodiments, probe beam 504 can include a
`
`wavelength in the visible, near-infrared, and/or infrared. For example, the wavelength of
`
`probe bearn 504can be about 780.2 nm, for example, when atomic vapor 511 comprises Rb.
`
`As shown in FIG. 5, pump and probe beams 502, 504 can propagate at small angle 505. In
`
`some embodiments, small angle 505 can be about 0.01 degrees to about
`
`| degrees. For
`
`example, small angle 505 can be about 0.5 degrees.
`
`{0053}
`
`Vapor cell 510 can be configured to enclose an atomic vapor 511, for example,
`vaporized Rb (e.g., Rb and/or ®’Rb). As shownin FIG. 5, vapor cell 510 can include atomic
`
`vapor 511, cylindrical wail 512, first window 516, second window518, heating system 520,
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`temperature sensing system 530, processor 540, and/or balanced differential detector 550.
`
`Cylindrical wall 512 can include exterior surface 513 and interior surface 515.
`
`In some
`
`embodiments, as shown in FIG. 5, pump beam 502, probe beam 504, and vapor cell 310 can
`
`be arranged in a forward-scattering geometry (e.g., forward-scattering geometry 400 shown
`
`in FIG. 4). In some embodiments, as shown in FIG. 5, vapor cell 510 can have a longitudinal
`
`length 514. In some embodiments, longitudinal Jength 514 can be about 0.5 cm to about 10
`
`cm. For example, longitudinal length 514 can be about 8 cm. In some embodiments, vapor
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`cell 510 can have a temperature (e.¢., internal) of about 30 °C to about 100 °C. For example,
`
`the temperature can be about 35 °C to about 45 °C.
`
`10054]
`
`Atomic vapor 511 can be configured to interact with overlapped pump and probe
`
`beams 502, 504 to generate (e.g., via DFWM) arnplified probe beam 506 and conjugate bearn
`
`508. In some embodiments, atomic vapor 511 can inchide a rubidium (Rb) vapor. In some
`
`embodiments, atomic vapor 511 can inchide an alkali metal (e.¢., sodium (Na), rubidium
`
`(Rb), caesium (Cs), etc.). Amplified probe beam 506 can be produced via DFWMand can
`
`have an output power of about 1 uWto about 15 mW. For example, probe beam 504 can be
`
`about 100 pWand amplified probe beam 506 can be about 1 mW, which corresponds to a
`
`gain of 10, where gain = (output power of amplified probe beam 506) / (input power of probe
`
`beam 504). Conjugate bearn 508 can be produced via DFWMand can have an output power
`
`of about 1 aWto about 15 mW. Output power of conjugate beam 508 can be approximately
`
`equal to (input probe beam 504) * (gain — 1).
`
`{0055}
`
`As shown in FIG. 5, cylindrical wail 512 can be disposed between first and second
`
`windows 516, 518 to enclose (e.g.
`
`seal under vacuum) atomic vapor S11.
`
`In some
`
`embodiments, cylindrical wall 512 can include copper, glass, and/or any other material with a
`
`high thermal conductivity. First and second windows 516, 518 can be configured to transmit
`
`(e.g., focus} pump and probe beams 502, 504 into atomic vapor 511 and transmit generated
`
`amplified probe beam 506 and conjugate beam 508 to balanced differential detector 550. In
`
`some embodiments, as shown in FIG. 5, first and second windows 516, 518 can be disks. In
`
`some embodiments, first and second windows 516, 518 can include an anti-reflection (AR)
`
`coating. For example, the AR coating can be a selective wavelength notch filter, for example,
`
`a bandpass filter of about 780.2 nm. In some embodiments, a focusing element and/or a lens
`
`(not shown) can be disposed near and/or integrated with first window 516 and can be
`
`configured to focus pump and probe beams 502, 504 into atomic vapor 411.
`
`10056]
`
`Heating system 520 can be configured to increase and/or decrease a temperature of
`
`vapor cell 510 and/or atornic vapor 511. Heating system 520 can include first and second
`
`heaters 522, 524 (e.¢., resistive coils} configured to provide heating (e.¢., resi