Damage-free single-mode transmission of deep-
`UV light in hollow-core PCF
`F. Gebert,1 M. H. Frosz,2 T. Weiss,2,3 Y. Wan,1
`A. Ermolov,2 N. Y. Joly,2 P. O. Schmidt,1,4,* and P. St. J. Russell2
`1QUEST Institute, Physikalisch-Technische Bundesanstalt, 38116 Braunschweig, Germany
`2Max Planck Institute for the Science of Light, Günther-Scharowsky-Str. 1, 91058 Erlangen, Germany
`34th Physics Institute and Research Center SCoPE, University of Stuttgart, Pfaffenwaldring 57, 70550 Stuttgart,
`Germany
`4Institut für Quantenoptik, Leibniz Universität Hannover, 30167 Hannover, Germany
`*piet.schmidt@quantummetrology.de
`
`Abstract: Transmission of UV light with high beam quality and pointing
`stability is desirable for many experiments in atomic, molecular and optical
`physics. In particular, laser cooling and coherent manipulation of trapped
`ions with transitions in the UV require stable, single-mode light delivery.
`Transmitting even ~2 mW CW light at 280 nm through silica solid-core
`fibers has previously been found to cause transmission degradation after
`just a few hours due to optical damage. We show that photonic crystal fiber
`of the kagomé type can be used for effectively single-mode transmission
`with acceptable loss and bending sensitivity. No transmission degradation
`was observed even after >100 hours of operation with 15 mW CW input
`power. In addition it is shown that implementation of the fiber in a trapped
`ion experiment increases the coherence time of the internal state transfer
`due to an increase in beam pointing stability.
`© 2014 Optical Society of America
`OCIS codes: (060.2280) Fiber design and fabrication, (060.4005) Microstructured fibers,
`(060.5295) Photonic crystal fibers, (020.1335) Atom optics.
`References and links
`1. C. W. Chou, D. B. Hume, J. C. J. Koelemeij, D. J. Wineland, and T. Rosenband, “Frequency comparison of two
`high-accuracy Al+ optical clocks,” Phys. Rev. Lett. 104(7), 070802 (2010).
`2. B. Hemmerling, F. Gebert, Y. Wan, D. Nigg, I. V. Sherstov, and P. O. Schmidt, “A single laser system for
`ground-state cooling of 25Mg+,” Appl. Phys. B 104(3), 583–590 (2011).
`3. T. Rosenband, D. B. Hume, P. O. Schmidt, C. W. Chou, A. Brusch, L. Lorini, W. H. Oskay, R. E. Drullinger, T.
`M. Fortier, J. E. Stalnaker, S. A. Diddams, W. C. Swann, N. R. Newbury, W. M. Itano, D. J. Wineland, and J. C.
`Bergquist, “Frequency ratio of Al+ and Hg+ single-ion optical clocks; metrology at the 17th decimal place,”
`Science 319(5871), 1808–1812 (2008).
`4. Y. H. Wang, R. Dumke, T. Liu, A. Stejskal, Y. N. Zhao, J. Zhang, Z. H. Lu, L. J. Wang, T. Becker, and H.
`Walther, “Absolute frequency measurement and high resolution spectroscopy of 115In+ 5s21 S0-5s5p 3P0
`narrowline transition,” Opt. Commun. 273(2), 526–531 (2007).
`5. A. C. Wilson, C. Ospelkaus, A. P. VanDevender, J. A. Mlynek, K. R. Brown, D. Leibfried, and D. J. Wineland,
`“A 750-mW, continuous-wave, solid-state laser source at 313 nm for cooling and manipulating trapped 9Be+
`ions,” Appl. Phys. B 105(4), 741–748 (2011).
`6. Y. Wan, F. Gebert, J. B. Wübbena, N. Scharnhorst, S. Amairi, I. D. Leroux, B. Hemmerling, N. Lörch, K.
`Hammerer, and P. O. Schmidt, “Precision spectroscopy by photon-recoil signal amplification,” Nat Commun 5,
`3096 (2014).
`J. P. Gaebler, A. M. Meier, T. R. Tan, R. Bowler, Y. Lin, D. Hanneke, J. D. Jost, J. P. Home, E. Knill, D.
`Leibfried, and D. J. Wineland, “Randomized benchmarking of multiqubit gates,” Phys. Rev. Lett. 108(26),
`260503 (2012).
`8. H. Häffner, W. Hänsel, C. F. Roos, J. Benhelm, D. Chek-al-Kar, M. Chwalla, T. Körber, U. D. Rapol, M. Riebe,
`P. O. Schmidt, C. Becher, O. Gühne, W. Dür, and R. Blatt, “Scalable multiparticle entanglement of trapped
`ions,” Nature 438(7068), 643–646 (2005).
`9. A. Friedenauer, H. Schmitz, J. T. Glueckert, D. Porras, and T. Schaetz, “Simulating a quantum magnet with
`trapped ions,” Nat. Phys. 4(10), 757–761 (2008).
`10. J. W. Britton, B. C. Sawyer, A. C. Keith, C. C. J. Wang, J. K. Freericks, H. Uys, M. J. Biercuk, and J. J.
`Bollinger, “Engineered two-dimensional Ising interactions in a trapped-ion quantum simulator with hundreds of
`spins,” Nature 484(7395), 489–492 (2012).
`
`7.
`
`#210864 - $15.00 USD
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`Received 24 Apr 2014; revised 23 May 2014; accepted 28 May 2014; published 17 Jun 2014
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`11. N. Yamamoto, L. Tao, and A. P. Yalin, “Single-mode delivery of 250 nm light using a large mode area photonic
`crystal fiber,” Opt. Express 17(19), 16933–16940 (2009).
`12. J. Nold, P. Hölzer, N. Y. Joly, G. K. L. Wong, A. Nazarkin, A. Podlipensky, M. Scharrer, and P. St. J. Russell,
`“Pressure-controlled phase matching to third harmonic in Ar-filled hollow-core photonic crystal fiber,” Opt. Lett.
`35(17), 2922–2924 (2010).
`13. J. C. Travers, W. K. Chang, J. Nold, N. Y. Joly, and P. St. J. Russell, “Ultrafast nonlinear optics in gas-filled
`hollow-core photonic crystal fibers [Invited],” J. Opt. Soc. Am. B 28, A11–A26 (2011).
`14. S. Février, F. Gérôme, A. Labruyère, B. Beaudou, G. Humbert, and J. L. Auguste, “Ultraviolet guiding hollow-
`core photonic crystal fiber,” Opt. Lett. 34(19), 2888–2890 (2009).
`15. J. C. Knight, T. A. Birks, P. St. J. Russell, and D. M. Atkin, “All-silica single-mode optical fiber with photonic
`crystal cladding,” Opt. Lett. 21(19), 1547–1549 (1996).
`16. F. Benabid and P. J. Roberts, “Linear and nonlinear optical properties of hollow core photonic crystal fiber,” J.
`Mod. Opt. 58(2), 87–124 (2011).
`17. B. Debord, M. Alharbi, T. Bradley, C. Fourcade-Dutin, Y. Y. Wang, L. Vincetti, F. Gérôme, and F. Benabid,
`“Hypocycloid-shaped hollow-core photonic crystal fiber Part I: arc curvature effect on confinement loss,” Opt.
`Express 21(23), 28597–28608 (2013).
`18. Y. Y. Wang, X. Peng, M. Alharbi, C. F. Dutin, T. D. Bradley, F. Gérôme, M. Mielke, T. Booth, and F. Benabid,
`“Design and fabrication of hollow-core photonic crystal fibers for high-power ultrashort pulse transportation and
`pulse compression,” Opt. Lett. 37(15), 3111–3113 (2012).
`19. J. L. Archambault, R. J. Black, S. Lacroix, and J. Bures, “Loss Calculations for Antiresonant Wave-Guides,” J.
`Lightwave Technol. 11(3), 416–423 (1993).
`20. J. Pomplun, L. Zschiedrich, R. Klose, F. Schmidt, and S. Burger, “Finite element simulation of radiation losses
`in photonic crystal fibers,” Phys. Status Solidi A 204(11), 3822–3837 (2007).
`21. I. H. Malitson, “Interspecimen Comparison of Refractive Index of Fused Silica,” J. Opt. Soc. Am. 55(10), 1205–
`1209 (1965).
`22. S. Février, B. Beaudou, and P. Viale, “Understanding origin of loss in large pitch hollow-core photonic crystal
`fibers and their design simplification,” Opt. Express 18(5), 5142–5150 (2010).
`23. S. Schneider and G. J. Milburn, “Decoherence in ion traps due to laser intensity and phase fluctuations,” Phys.
`Rev. A 57(5), 3748–3752 (1998).
`24. R. Ozeri, W. M. Itano, R. B. Blakestad, J. Britton, J. Chiaverini, J. D. Jost, C. Langer, D. Leibfried, R. Reichle,
`S. Seidelin, J. H. Wesenberg, and D. J. Wineland, “Errors in trapped-ion quantum gates due to spontaneous
`photon scattering,” Phys. Rev. A 75(4), 042329 (2007).
`25. J. P. Gaebler, A. M. Meier, T. R. Tan, R. Bowler, Y. Lin, D. Hanneke, J. D. Jost, J. P. Home, E. Knill, D.
`Leibfried, and D. J. Wineland, “Randomized benchmarking of multiqubit gates,” Phys. Rev. Lett. 108(26),
`260503 (2012).
`26. Y. Colombe, D. H. Slichter, A. C. Wilson, D. Leibfried, and D. J. Wineland, “Single-mode optical fiber for high-
`power, low-loss UV transmission,” arXiv preprint, http://arxiv.org/abs/1405.2333 (2014).
`1. Introduction
`Standard solid-core silica optical fibers are ideal for low-loss delivery of single-transverse-
`mode beams from the visible to the infrared spectral range. There are, however, a number of
`applications in which single-mode delivery of ultraviolet (UV) light by fiber would be highly
`desirable. For example, experiments on coherent manipulation of trapped ions for precision
`spectroscopy and optical clocks [1–6], quantum information processing [7, 8] and trapped ion
`simulators [9, 10] all require stable laser intensity at the position of the ions. This can be
`achieved through good beam quality and pointing stability as provided by single-mode optical
`fibers. In view of the higher fidelity of coherent manipulations with stable single-mode fiber
`beam delivery, a trade-off in laser power is acceptable, in particular, since high power laser
`systems are readily available [2, 5]. A number of problems arise, however, when using
`standard optical fibers in the UV. Although single-mode guidance can be maintained (for the
`same core-cladding index step) simply by reducing the core diameter by the ratio of the
`wavelengths, or by using an endlessly single-mode solid-core photonic crystal fiber (PCF),
`most glasses become highly absorbing in the UV, and furthermore the transmission degrades
`over time due to UV-induced color center formation and optical damage in the core. For
`example, Yamamoto et al. found that in a PCF with a solid silica core the transmission
`dropped by more than 90% after ~4 hours when using 3 mW CW light at 250 nm [11].
`Recent experiments on nonlinear spectral broadening in gas-filled hollow core kagomé-
`style PCF have shown that these fibers are able to guide ultrashort pulses of UV light with
`losses of order 3 dB/m [12]. Other experiments have demonstrated single-mode beam quality
`at average powers of ~50 μW and finite element simulations indicate that the light-in-glass
`fraction in kagomé-PCF is typically <0.01% [13], which circumvents the problem of UV-
`
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`Received 24 Apr 2014; revised 23 May 2014; accepted 28 May 2014; published 17 Jun 2014
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`induced long-term damage in the glass. Kagomé-PCF can also be made effectively single-
`mode by decreasing the core size until higher-order modes have significantly higher
`propagation losses than the fundamental mode. A kagomé-PCF with 2 dB/m loss at 355 nm
`was recently demonstrated, but due to the relatively large core (~30 µm) it was highly
`multimode [14].
`In this letter we report the fabrication of a series of kagomé-PCFs with core diameters of
`~20 µm. The transmission loss was measured at 280 nm using the cut-back technique, and the
`output beam quality evaluated under varying in-coupling conditions. Simulations of the loss,
`together with transmission measurements, indicate that it is polarization-dependent and
`limited by fabrication-induced variations in the thickness of the core-wall surround. In
`particular, we show for the first time that few-m lengths of these fibers are capable of
`transmitting continuous wave UV powers of several mW without degradation. Finally, we
`show that use of kagomé-PCF in a trapped ion experiment significantly increases the
`coherence times of the internal state transfer due to a reduction in beam-pointing instabilities.
`2. Theory and methods
`The kagomé-PCFs were fabricated using the stack-and-draw technique [15]. Scanning
`electron micrographs (SEM) of one fiber are shown in Fig. 1. By careful control of the
`pressure applied to the core during drawing, samples with different core diameters and wall
`thicknesses could be obtained. By achieving fiber structures (most importantly the core
`diameter) that are scaled down significantly compared to the fiber structure in Ref [14], the
`kagomé-fibers are effectively single-mode even at the UV wavelengths considered here (~280
`nm).
`
`
`
`Fig. 1. (a) Scanning electron micrograph (SEM) of fiber sample A. (b) Close-up of the core
`structure of Fiber A with core-wall thickness measurements. The core diameter (measured flat-
`to-flat) is ~19 µm. (c) Similar close-up for Fiber B, with flat-to-flat core diameter of ~20 µm.
`Kagomé-PCFs typically guide light with a few dB/m loss over broad transmission
`windows (several hundred nm), interspersed with narrow bands of high loss [16]. Recently,
`kagomé-PCFs with modified shape of the core surround have been demonstrated with a loss
`of only tens of dB/km over broad transmission bands covering the red and the infrared
`spectral regions [17, 18]. The guiding mechanism in the low-loss regions is not yet fully
`elucidated, but appears to be a two-dimensional generalization of the ARROW mechanism
`previously studied in planar and cylindrical structures [19]. The principal high loss bands
`occur at wavelengths where the core mode phase-matches to modes guided in the core wall,
`i.e., when [16, 19]:
`
`
`
`
`
`λ) −
`
`(
`
`n
`
`=
`
`k h
`n
`2
`2
`cw
`g
`m
`where nm is the modal index (slightly less than 1 for the fundamental mode), hcw is the core-
`wall thickness, k = 2π/λ is the vacuum wavevector and ng(λ) is the wavelength-dependent
`refractive index of the glass.
`We calculated the fiber loss using finite-element modelling (FEM) [20], including the
`dispersion of the silica glass [21]. To reduce computational complexity the kagomé structure
`
`
`
`q
`
`π q, =
`
`
`
`1,2,3...
`
`
`
`(1)
`
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`Received 24 Apr 2014; revised 23 May 2014; accepted 28 May 2014; published 17 Jun 2014
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`was simplified to only one ring of air-holes around the core (inset of Fig. 2). Comparisons
`with simulations for the full kagomé-structure showed that this approximation works well, at
`least within the low-loss windows. It also accurately predicts the position and width of the
`high loss bands, although not the peak loss values.
`At a wavelength of 280 nm Eq. (1) predicts for m = 2 a high loss peak at a wall thickness
`of hcw = 252 nm, in agreement with the results of FEM (Fig. 2). Also for m = 2 one finds from
`Eq. (1) that dλ/dhcw ~1.1, indicating that a 1 nm variation in core-wall thickness will cause a
`~1 nm shift in the m = 2 resonance. Since the variations in the actual fibers are much greater,
`this will cause strong inhomogeneous broadening of the loss peak. Azimuthal variations in
`core-wall thickness will also break the six-fold symmetry of the structure and cause
`birefringence and polarization-dependent loss.
`As shown in Fig. 1(b), careful analysis of the SEMs shows that the core-wall thickness hcw
`for fiber A varies over the range 240 ± 20 nm and for fiber B over the range 205 ± 15 nm. A
`fixed wavelength of 280 nm and a core diameter of 2rco = 18.7 µm (corresponding to fiber A)
`was used in the FEM, which were for an ideal structure with a constant core-wall thickness. A
`realistic structure with azimuthal variations in core-wall thickness may display additional
`losses. The results are shown in Fig. 2. Within the measured range of core-wall thicknesses
`for fiber A, the loss can potentially reach above 100 dB/m. For fiber B, the calculated
`maximum loss can reach slightly above 1 dB/m.
`
`
`Fig. 2. The loss of LP01-like modes at λ = 280 nm in the simplified kagomé-structure shown in
`the inset, plotted against core-wall thickness. The main loss resonance according to Eq. (1)
`occurs at hcw≈255 nm (black dotted line). The results were calculated numerically using FEM.
`The accuracy of the calculation is limited to loss values above 0.001 dB/m.
`In Fig. 2 the main loss peak centered at hcw ~255 nm corresponds to the m = 2 solution of
`Eq. (1). Most of the additional loss peaks are caused by phase-matching to resonances in the
`complex cladding structure beyond the core surround. This effect is neglected in the
`derivation of Eq. (1) using simplifying approximations. Some of the loss peaks may also be
`related to the non-circular shape of the core-wall (a circular core-wall is assumed in deriving
`Eq. (1)), as was suggested in a theoretical study of a similarly simplified kagomé structure
`[22]. Consequently, the fine structure of the main loss peak and the additional loss peaks can
`only be captured within a FEM simulation. The closely spaced loss peaks found in Fig. 2
`demonstrate that even though certain values of core-wall thickness would theoretically give
`very low loss (<0.001 dB/m), the loss will in practice be higher due to nm-scale variations in
`core-wall thickness in the actual fibers.
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`3. Experimental results
`A fiber laser emitting at 1121 nm was frequency-quadrupled to produce up to 20 mW at 280
`nm [2]. After spatial filtering to clean up the beam profile, the light was focused to a beam-
`waist of 15 µm using a lens of focal length 75 mm and launched into the fiber.
`3.1 Loss, bending and polarization properties
`The loss was measured using a multiple cut-back technique, without changing the fiber in-
`coupling and keeping the fiber as straight as possible so as to minimize bending loss. The
`results are shown in Fig. 3(a). Fiber A had a measured core-wall thickness in the range ~220-
`260 nm (Fig. 1(b)), and yielded a loss of ~3 dB/m, whereas for fiber B the measured loss was
`~0.8 dB/m for a core-wall thickness in the range 190-220 nm. The strong sensitivity of loss
`resonances to the core-wall thickness as shown in the FEM simulation results of Fig. 2
`together with the azimuthal asymmetry of core-walls and their expected variation along the
`actual fiber do not allow a direct quantitative comparison between experiment and simulation.
`However, the measured losses are compatible with the simulated losses. In particular, the
`fiber with smaller core-wall thickness exhibits lower losses, since it is further away from the
`main loss resonance around hcw = 255 nm.
`
`
`
`Fig. 3. (a) Cut-back loss measurement for fiber A (blue dots) and fiber B (black stars) at a
`wavelength of 280 nm. The dB scale is normalized so that 0 dB corresponds to the transmitted
`power of the shortest fiber piece used in each cut-back measurement. The linear fits correspond
`to 2.9 dB/m (blue, fiber A) and 0.8 dB/m (black, fiber B). (b) Normalized transmission (center
`= 0.7) plotted radially versus orientation of the linearly polarized input light for 1 m long
`fibers. The measurement on fiber A (blue dots) exhibits a consistent maximum polarization-
`dependent loss of ~20%. An equivalent measurement for fiber B (black stars) showed a
`maximum polarization dependent loss of ~10%.
`Several mW of power at 280 nm was transmitted, typically ~48% of the launched power
`for fiber A (~1 m fiber length) and ~70% for fiber B (~1.3 m length). Bending was found to
`cause large variations in the transmitted power, probably due to enhanced leakage into the
`cladding and coupling to high-loss higher-order modes. However, we found no bending loss-
`induced degradation in transmission for fibers which were kept either straight or at bend-radii
`larger than 20 cm. To quantify the bend-sensitivity for smaller bending radii the output power
`was measured while winding fiber A around a mandrel. The transmitted power exhibited
`strong fluctuations depending on the exact position and twist of the fiber. We believe that this
`additional loss is caused by geometrical deformation during bending of the fiber. To minimize
`this effect, the output power was recorded while rearranging the fiber and the maximum
`measured power was used to derive the bending loss. A fit to the relative transmission for
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`Received 24 Apr 2014; revised 23 May 2014; accepted 28 May 2014; published 17 Jun 2014
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`different numbers of wrapping turns led to a loss of 2.9 dB/turn for a bending radius of 1.6 cm
`and a loss of 2.7 dB/turn for a bending radius of 4.0 cm. The similarity of these values might
`be due to different remaining contributions from the loss caused by geometrical deformation.
`A more elaborate method excluding this additional loss would be necessary to resolve this
`issue.
`It was also found that the transmission depends on the polarization state of the light. This
`is normally not expected in kagomé-PCFs with perfect six-fold symmetry, but as was shown
`with simulations in the previous section (see Fig. 2), the loss is sensitive to nm-scale
`variations in core-wall thickness. Azimuthal variations in core-wall thickness can therefore
`result in polarization-dependent loss. In Fig. 3(b) the normalized transmission along 1 m
`lengths of fiber is plotted while varying the linear input polarization. There is a maximum
`~20% (~1 dB/m) difference in output power between orthogonal polarizations for fiber A, and
`a maximum ~10% (~0.5 dB/m) difference for fiber B. We verified that this effect was due to
`the structure of the fiber by rotating the fiber in the setup. This rotated the shape of the
`polarization dependence of the loss, supporting that the effect was indeed due to the structure
`of the fiber. Given the high sensitivity of loss on the core-wall thickness (Fig. 2), the observed
`~10-20% variation in transmission is compatible with the observed azimuthal asymmetry in
`core-wall thickness (Fig. 1(b, c)) Other asymmetries in the structure (e.g. small variations in
`core-wall length) could also play a role.
`3.2 Output beam quality
`The robustness of the single-mode guidance was tested by monitoring the output beam profile
`while translating the input coupling beam across the input face of the fiber. Little evidence of
`higher-order modes was observed (Fig. 4). We note that in Ref [14]. the 355 nm light output
`from a fiber with ~30 µm core diameter showed a highly multimoded pattern. The kagomé-
`PCFs considered here are effectively single-mode due to a smaller core diameter (~20 μm).
`Therefore higher-order modes experience larger propagation losses, which means that the
`fibers act as mode-cleaners.
`
`
`Fig. 4. Measured near-field intensity profiles from fiber A for different transverse positions of
`the input beam. The coordinates refer to the horizontal and vertical displacements (in µm) of
`the focused laser spot from the core center. The intensity profiles are not perfectly symmetrical
`with respect to off-center displacements; this could both be due to asymmetry in the fiber
`structure as well as because the transverse position could not be controlled to better than ~1
`µm.
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`3.3 Lifetime investigation
`As mentioned in the introduction there is a current need for optical fibers that can deliver UV
`light with high beam quality without degradation due to UV-induced damage to the glass
`core. Experiments with a solid-core PCF showed that the transmission of 280 nm light
`dropped by more than 80% after 3 hours at a CW power level of only 2 mW, in line with
`previous reports [11].
`
`
`Fig. 5. Relative transmission in the kagomé-PCF over time when 15 mW of 280 nm CW light
`is coupled into the fiber.
`FEM calculations indicate that less than 0.01% of the light in a perfect kagomé-PCF is
`guided in the glass [13], which suggests that UV-induced damage should be largely
`eliminated. To investigate this we launched 15 mW of 280 nm CW light into fiber A and
`monitored the transmission continuously over time. As shown in Fig. 5, there are no signs of
`UV-induced damage over the 14 hours of continuous measurements. We additionally made
`experiments in which the kagomé PCF was left to transmit around 50% of more than 15 mW
`input UV light for altogether more than 100 hours. Within measurement error we could not
`detect a change in the transmission over this time period.
`4. Applications
`In order to study the applicability of the fiber in trapped ion experiments, an intensity
`stabilization set-up was implemented. The ends of two 1.2 m long pieces of fiber B were fixed
`with adhesive tape in V-grooves of an aluminum block. The fibers were used to replace two
`periscope systems that connected two stacked platforms. The beam was widened to a waist of
`approximately 0.7 mm and then focused down using a lens with a focal length of 75 mm.
`With this simple setup we achieved typically more than 50% transmission through both fibers
`using approximately 5 mW of input power. The incoupling efficiency is limited by poor beam
`quality in front of the fiber. The distance from the output face of the fibers to the trapped ion
`was kept as short as possible so as to minimize residual pointing fluctuations from air
`currents.
`Pointing instabilities lead to intensity fluctuations at the position of the ion and can
`therefore limit the laser control of its internal state. For coherent manipulation of the ion we
`used a Raman beam configuration to excite the |F = 3, mF = 3 = |↓ ↔ |F = 2, mF = 2 = |↑
`transition in the 2S1/2 state of a 25Mg+ ion via near-resonant Raman coupling detuned by 9.2
`GHz to the 2P3/2 excited state [2]. Here, F denotes the total angular momentum and mF its
`projection along the magnetic field direction. These so-called qubit states are separated by a
`hyperfine splitting of 1.789 GHz and further split by an external bias magnetic field that lifts
`the degeneracy of the magnetic sub-states. The Raman beams were generated by frequency
`
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`Received 24 Apr 2014; revised 23 May 2014; accepted 28 May 2014; published 17 Jun 2014
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`quadrupling the output of a fiber laser at 1118 nm to 280 nm. After splitting the UV light into
`two beams each one passed through several acousto-optical modulators (AOMs) to bridge the
`frequency difference between the two qubit states. The complete optical set-up and the level
`scheme of 25Mg+ are described in [2]. Since no single-mode fibers were previously available
`at a wavelength of 280 nm, the original set-up consisted of free-space beam-paths
`approximately 5 m long. Air turbulence and small vibrations of mirrors and other optical
`components led to noticeable pointing fluctuations at the position of the ion. Furthermore, the
`AOMs distorted the beam shape, which caused additional intensity gradients across the beam
`profile. These were cleaned to a near-Gaussian transverse mode shape using the hollow core
`kagomé-PCFs discussed here.
`The effect of beam-pointing fluctuations was investigated by measuring the signal contrast
`for laser-driven coherent internal state oscillations both with and without a kagomé-PCF. To
`this end we recorded the internal state of the ion after coupling the two hyperfine states via the
`Raman lasers for different pulse durations (Rabi flopping). The excitation probability is
`determined by averaging the result of approximately 250 repetitions of the experiment per
`Raman interaction time. If the position of the laser beam and therefore the light intensity on
`the ion fluctuates, the Rabi frequency (which is a function of the laser intensity) will change
`between subsequent experiments. During the averaging process this results in a reduction of
`the measured Rabi oscillation contrast, which can be described as a damped oscillation of the
`ground state population [23]:
`
`
`
`( )
`P t
`↓
`
`=
`
`2 1
`
`1
`
`
`γ−
`t
`
`+
`
`e
`
`cos
`
`(
`
`)
`
`t
`
`0
`
`
`,
`
`
`(2)
`
`γ= ΓΩ
` the decay rate of the Rabi oscillations, and
`where Ω0 is the mean Rabi frequency,
`/ 2
`Γ a scale-factor for the intensity noise. Competing effects that reduce the Rabi oscillation
`contrast further are the motional excitation of the ion in the trap due to its non-zero
`temperature, and off-resonant scattering of the Raman beams [24]. Off-resonant scattering is
`not a fundamental limitation, since it can be mitigated by detuning the Raman resonance
`further from the atomic transition. Preparation of the ion close to the motional ground state of
`the |↓-state, via Raman sideband cooling [2] at the beginning of each experimental cycle,
`eliminates the influence of motional excitation on the Rabi-flopping contrast. After cooling to
`±
`n =
` where n is the mean motional quantum
`a mean motional excitation of
`0.02 0.02,
`number, we applied the Raman coupling for different pulse durations while actively
`stabilizing the intensity of the Raman lasers using a sample-and-hold intensity stabilization
`circuit.
`Figure 6 shows experimental data for the Rabi flopping curves with and without the
`kagomé-PCF, together with a corresponding fit according to Eq. (2). The extracted decay rate
`γ is shown in Fig. 6 and is averaged over 7 different measurements in each configuration. The
`resulting weighted average of the decay rates is 4.1 ± 0.1 ms−1 with, and 8.5 ± 0.6 ms−1
`without the kagomé-PCF in place. The relatively strong residual decay is dominated by off-
`resonant excitation of the ion to the electronically excited 2P3/2 state, due to the limited Raman
`detuning of 9.2 GHz. This is confirmed in an independent experiment in which we initially
`prepared the ion in one of the two qubit states and then applied the Raman lasers detuned to
`the two-photon resonance by half the distance to the next resonance (1.1 MHz). Subsequent
`measurements of the internal state of the ion yielded the decay rates of the two states due to
`off-resonant excitation γ|↓ = 1.1 ± 0.1 ms−1 and γ|↑ = 4.4 ± 0.4 ms−1, which are comparable to
`the residual decay rate of the Rabi oscillation with the kagomé-PCF in the set-up in Fig. 6(b).
`Further investigations at a larger Raman detuning would be necessary to determine the
`ultimate limit of residual Rabi frequency fluctuations.
`
`20
`
`#210864 - $15.00 USD
`
`Received 24 Apr 2014; revised 23 May 2014; accepted 28 May 2014; published 17 Jun 2014
`
`(C) 2014 OSA
`
`30 June 2014 | Vol. 22, No. 13 | DOI:10.1364/OE.22.015388 | OPTICS EXPRESS 15395
`
`Agilent Exhibit 1263
`Page 8 of 9
`
`Ω
`

`

`
`
`Fig. 6. Raman Rabi oscillations (a) without kagomé-PCF and (b) with kagomé-PCF in the set-
`up. The decay rate is extracted from a fit to Eq. (2) and the mean value over 7 measurements
`is displayed in the corresponding graphs. The residual decay is dominated by off-resonant
`excitation from the Raman lasers due to the limited Raman detuning of 9.2 GHz.
`The experimental results indicate that kagomé-PCF will significantly reduce one of the
`dominant errors in coherent manipulation of trapped ions [25]. An additional advantage of
`adding the kagomé-PCF to this type of set-up for single ion experiments is that any
`realignment of the beam-path before the fiber does not shift the focal position on the ion,
`which is typically cumbersome to achieve in free-space set-ups.
`5. Conclusions
`Kagomé-style photonic crystal fibers provide high-quality single-mode transmission at 280
`nm wavelength with losses of ~1 dB/m. The transmitted beam is free of laser pointing
`instabilities and unlike in solid-core fibers there is no perceptible drop in transmission due to
`UV-induced damage, even after 100 hours of operation at 15 mW. We note that an alternative
`approach, based on hydrogen-loading of a solid-core photonic crystal fiber, has recently been
`reported [26].
`Acknowledgments
`F. Gebert, Y. Wan and P.O. Schmidt acknowledge support by DFG through QUEST and
`SCHM2678/3-1. Y. Wan acknowledges support from IGSM.
`
`
`#210864 - $15.00 USD
`
`Received 24 Apr 2014; revised 23 May 2014; accepted 28 May 2014; published 17 Jun 2014
`
`(C) 2014 OSA
`
`30 June 2014 | Vol. 22, No. 13 | DOI:10.1364/OE.22.015388 | OPTICS EXPRESS 15396
`
`Agilent Exhibit 1263
`Page 9 of 9
`
`