High-visibility large-area atom interferometry

Transcription

1 High-visibility large-area atom interferometry Benjamin Plotkin-Swing, Daniel Gochnauer, Katherine McAlpine, and Subhadeep Gupta Department of Physics, University of Washington, Seattle, Washington 98195, USA (Dated: December, 17) Here C(t) is the signal envelope related to the coherence of the source and φ i (t) are the phases accumulated by the different paths. Relative to path, paths 1 and 3 accumulate phase from their kinetic energies and thus S(t) oscillates at a frequency of 8ω rec, where ω rec = k /m is the recoil frequency and m is the mass of the atom. Importantly, effects from mirror vibrations on the optical standing wave phases cancel in this expression. Distinct from earlier realizations [, 3], a dramatic enhancement of phase accumulation of 1 n ω rec T is achieved in this work due to the scalable application of multiple acceleration pulses. Our atom source consists of ytterbium ( 174 Yb) BECs of 15, atoms which we prepare in a crossed-beam optical dipole trap operating at 53 nm. After condensate formation, we decompress the trap to a mean frequency of ω = π 63 Hz. To reduce the density and atomic interactions further, we allow ms time-of-flight after trap turn-off before beginning the interferometry sequence. Our atom optics consist of diffraction beams near the 1 S 3 P 1 (λ g = 556 nm = π/k, Γ g = π 18 khz) intercombination transition and a readout beam near the 1 S 1 P 1 (λ b = 399 nm, Γ b = π 8 MHz) transition, both of which are derived from our Yb laser cooling sources. The two diffraction beams are detuned from the atomic resonance by g /Γ g +13 and counterpropagate horizontally to form a standing wave. For prearxiv: v1 [physics.atom-ph] 19 Dec 17 We demonstrate phase-stable high-visibility atom interferometry for up to 11 photon recoil momenta (11 k) path separation. The signal visibility of 3% at the largest separation greatly exceeds the performance of earlier free-space interferometers. In addition to the symmetric interferometer geometry and Bose-Einstein condensate source, the robust scalability of our approach relies crucially on the suppression of undesired diffraction phases through a careful choice of atom optics parameters. The interferometer phase evolution is quadratic with number of recoils, reaching a rate as large as radians/s. We discuss the applicability of our method towards a new measurement of the fine-structure constant and a test of QED. The precision of atom interferometry methods [1] can be fruitfully directed towards applications such as inertial sensing [ 5], and fundamental physics such as tests of the equivalence principle [6, 7] and of quantum electrodynamics (QED) [8]. Light-pulse interferometers, central to these endeavors, operate by using standing-wave optical pulses as beamsplitters and mirrors, which impart momenta in units of photon momentum k to the atoms. Such interferometers gain in measurement sensitivity by the increase of the enclosed space-time area with momentum-boosting acceleration pulses [9, 1]. Phasestable interferometers with large momentum separation are thus an overarching goal in atom interferometry. Path separations n k with n up to 1 have been demonstrated [1], however interferometer phasestability [11] was not observed due to technical noise from mirror vibrations. Vibration-immunity and resultant phase-stability can be recovered by operating two simultaneous interferometers in a conjugate or dual geometry [1, 1]. However the operation of such interferometers has been limited to n 3 [1, 13, 14]. Visibility of 7% has been reported for n = 8 in a guided atom interferometer [15], but such methods have to contend with the additional systematic effects from a confining potential. In this paper we demonstrate phase-stable and scalable atom interferometry with very large momentum separation (n > 1 photon recoils), achieving 3% visibility at the largest n = 11. The resulting interferometer phase grows quadratically with momentum, reaching a rate as high as radians/s. Undesirable diffraction phases are theoretically and experimentally analyzed and kept under control by our choice of atom-optics parameters. When applied to a precision measurement for the finestructure constant α and test of QED, our interferometer demonstrates a favorable scaling. Our techniques for high signal visibility and suppressed diffraction phases for large n interferometers should also positively impact other applications of atom interferometry including inertial sensing [ 5], measuring gravity [16 18] and the Newtonian gravitational constant [19, ]. Our contrast interferometer (CI), (Fig. 1) operates on a Bose-Einstein condensate (BEC) atom source and consists of four atom-optics elements: splitting pulse, mirror pulse, acceleration pulses, and readout pulse. The splitting pulse places each atom into an equal superposition of 3 momentum states: + k, k, and k, referred to as paths 1,, and 3 respectively. The mirror pulse reverses the momenta of paths 1 and 3 from ± k to k. The acceleration pulses increase the momentum separation of paths 1 and 3 to a variable amount n k during two sets of free evolution times T. After the final deceleration sequence brings the outer paths back to ± k, all three paths overlap in space and form an atomic density grating whose amplitude varies in time. By pulsing on a traveling readout laser beam and collecting the Bragg-reflection off this matter-wave grating we obtain the characteristic CI signal: S(t) = C(t)cos ( φ 1 (t) + φ 3 (t) ) φ (t) (1)

2 FIG. 1: (a,b) Space-time trajectory (to scale) and atom optics sequence for the n = 16 and n = 1 contrast interferometer (CI) with T = 1 ms. The shaded regions indicate that some pulses (black shading) affect both moving paths, while others (orange and blue shading) affect a single path. The CI signal is acquired by applying a traveling wave laser pulse (violet shading) and collecting the Bragg-reflected optical signal on a photo-multiplier tube (PMT). Readout signals (violet) with fits (dashed black) for various momentum splittings n are shown in (c,d) ( shot averages), and (e,f) (8 shot averages); (c) has 88% visibility (based on the fit), and (f) has 3% visibility with n = 11. cise relative frequency control, each beam is derived from the first diffraction order of a MHz acousto-optic modulator (AOM) driven by an Analog Devices AD991 direct digital synthesizer. Each AOM output is passed through a polarization-maintaining single mode fiber to ensure a clean Gaussian mode and a stable linear polarization. The diffraction beams have a waist of 1.8 mm, allowing lattice depths of up to 5 ω rec at the atoms for the available power. We stabilized the diffraction beam intensities by feeding back to the AOMs, keeping fluctuations in the diffraction pulse peak lattice depth to %. The splitting pulse has a width of 7µs, and operates within the Kapitza-Dirac regime [4]. The mirror pulse is a second-order Bragg π pulse with Gaussian 1/e fullwidth 54µs and peak lattice depth 14 ω rec. Each acceleration pulse is a third-order Bragg π pulse delivering 6 k of momentum, with Gaussian 1/e full-width 54µs and peak lattice depth 6.6 ω rec. We accelerate the outer paths sequentially as shown in Fig. 1(a,b) with successive third-order π pulses separated by 13 µs. Although this sequential acceleration scheme breaks the symmetric form of the interferometer, the suppression of systematic effects from the symmetry of the three-path geometry [, 3] is still largely retained if the time between acceleration pulses for paths 1 and 3 is short, as in our case. We use light at λ b (399nm) for the readout beam which Bragg reflects at 44 degrees from the λ g / = 78 nm period matter wave grating to form the CI signal, and eliminates many signal-to-noise issues associated with stray reflections when using Bragg back-scattering at 556nm as in earlier work [3]. Figure 1(c-f) shows contrast readout signals for various values of n, each of which is an average of multiple experimental iterations (shots). The phase stability of the interferometer is apparent in the high visibility of these fringes even for the largest (n = 11) momentum splitting used in this work. To our knowledge, this is the highest momentum splitting in any atom interferometer that produces stable visible fringes. We attribute this capability to the inherent vibration insensitivity of the CI and the suppression of diffraction phases as discussed below. Note that these results are obtained without any active vibration isolation. To extract fringe visibility, we fit these averaged signals with the expression C(t r )cos (4ω rec t r + Φ) + S using the currently-accepted value of ω rec and a Gaussian envelope C(t r ) [5]. Here t r is the time from the start of the readout pulse and S is a vertical offset. The visibility of our signal (Fig. (a)) is defined as [(Max-Min)/(Max+Min)] 1, where Max and Min are determined by our fitted values for the vertical offset and peak envelope amplitude. The signal vertical offset is due to the 7% spontaneous scattering probability from the readout pulse which is detuned by b /Γ b = 5. We analyze single experimental shots by extracting the amplitude and phase of the Fourier component at 8ω rec. Figure (a) shows how the amplitude, relative to the smallest n interferometer, varies with n. We find that our data is well described by a simple model based on finite acceleration pulse efficiency. The fraction of atoms

3 3 remaning in path 1 or 3 that contribute to the final CI signal is A ζ, where A is the efficiency per k of our acceleration pulses, and ζ = 4(n 4) is the total number of photon recoils from the acceleration pulses only, for path 1 or 3. A fit to the amplitude data using this model (Fig. (a)) returns A =.9845(), or 91% per third-order Bragg pulse, consistent with a direct measurement of our π-pulse efficiency from absorption imaging of the atoms. This amplitude model together with the signal vertical offset from spontaneous scattering [6], yields a visibility model which captures all the main features of our data (dashed blue line in Fig. (a)). The phase-stability of the interferometer is characterized by the standard deviation of extracted single-shot phases (Fig. (b)), which is around.1 rad for low n, growing to.6 rad for the largest n. The calculated reduction in visibility due exclusively to these phase fluctuations (dotted green line in Fig. (a)) is negligible compared to the effect from the decreasing amplitude. We conclude that the current limitation in reaching even higher n is the acceleration pulse efficiency, which can be improved in future setups. For a free evolution time of T, we define the signal phase at the start of the readout pulse to be the CI phase Φ(T ) = 1 n ω rec T +Φ offset. Here Φ offset contains a number of phase shifts that are common to interferometers of different T, as well as contributions from systematic effects. The evolution of the CI phase Φ with time is Signal Visibility and Relative Amplitude (%) δφ(rad) Amplitude Visibility Visibility, corr Φ sdev Φ sdev, corr (a) (b) n ( hk) FIG. : (a) Normalized readout signal amplitude and visibility vs n. The amplitude is based on the Fourier component at 8ω rec, and visibility is extracted from sinusoidal fits to averaged data as shown in Fig. 1. Signal visibility is calculated with (black triangles) and without (blue squares) the diffraction phase correction. The solid orange line is a fit to the observed amplitude and the dashed and dotted lines are model curves (see text). (b) CI phase standard deviation vs n, with (black diamonds) and without (blue circles) the diffraction phase correction. Φ (rad) Residuals (rad) (a) (c) dφ/dt (1 7 rad/s) 6 4 (b) n ( hk) Free evolution time (ms) FIG. 3: (a) CI phase Φ vs free evolution time T with linear fit, for various n. (b) Fit slopes dφ/dt vs n, demonstrating the expected quadratic relationship dφ/dt = 1 n ω rec (black curve). (c) Typical fit residuals (n = 16). shown in Fig. 3 for various n. The fitted slopes are in good agreement with the expected dφ/dt = 1 n ω rec and may be used to precisely measure ω rec. The quadratic scaling of the CI phase with n is a distinct benefit for precision measurements, however it comes at the cost of a systematic effect from diffraction phases. This effect stems from momentum-dependent phase shifts during Bragg diffraction and can be significant for different interferometer geometries [3, 7 9]. A critical gauge of the viability of the CI scheme is therefore the scaling of the diffraction phase with large momentum separation. An important element for our favorable n scaling was the selection of acceleration pulse parameters that suppressed the diffraction phase contributions to the CI phase fluctuations, in addition to providing good atom optics efficiency. The presence of an optical lattice modifies the atomic dispersion relations leading to momentum-dependent (and therefore path-dependent) phase shifts which affect the CI signal according to Eqn.1. We experimentally characterized the diffraction phase effect for our acceleration and mirror pulse parameters by varying the peak pulse intensity around the π pulse condition (π point) and observing the variation of the CI phase. As shown in Fig. 4, our observations agree well with a numerical model of the diffraction processes which is equivalent to those described in [3, 8]. The diffraction phase from the splitting pulse is negligible and the diffraction phases at the π points for the Bragg mirror and acceleration pulses constitute a T -independent offset to the CI phase. Thus, in standard interferometer operation we need only consider the variations of the diffraction phase around the π point from the intensity fluctuations of our lattice.

4 4 The black curve in Fig. 4 implies that % intensity variations (our upper bound) in the mirror pulse contribute 7 mrad to the CI phase standard deviation. The first acceleration pulse contributes about 5 mrad (blue curve), while for larger n the behavior converges to the dotted orange curve. For the largest n = 11 interferometer there is less than mrad diffraction phase fluctuations per shot, including the effects from all the pulses. The operation of the interferometer with the chosen parameters for the acceleration π-pulses is crucial for its scalability. For instance, pulse widths four times longer lead to order of magnitude greater diffraction phases, which we have verified both experimentally and theoretically. The CI phase fluctuations can be improved by applying a shot-by-shot diffraction phase correction based on the correlation between the CI phase and the recorded diffraction pulse amplitudes. The correction is significant, reducing the phase noise to < 3 mrad for n up to 88 (Fig. (b)). We also observe a small improvement in the visibilities of the corrected averaged data (Fig. (a)). We have considered the effects from atomic interactions on our results. Our condensate source is in the Thomas-Fermi regime and its time-of-flight expansion can be analyzed accordingly [3, 31]. The estimated phase fluctuations arising from the < 3% fluctuations in initial splitting asymmetry are far less than those observed in Fig. (b). The remaining phase fluctuations in Fig. (b) are likely due to momentum transfer timing variations caused by shot-to-shot fluctuations in the time-varying Rabi frequencies of the acceleration pulses. This effect, which grows with n, can be reduced in future setups with more robust stabilization methods for the diffraction pulses. We now turn to the application of the large n CI technique towards a photon recoil and α measurement. The precision in ω rec can be written as: δω rec = δφ ω rec Φ = δφ 1 n ω rec T M where T is the range of free evolution times over which the slope of Φ(T ) is measured, δφ is the uncertainty in the measured CI phase, and M is the number of experimental shots. In our current CI setup, the free evolution time is constrained by the atoms falling out of the horizontally oriented diffraction beams, and 1 n ω rec T is optimized to radians for n = 76, and T = 3 ms. This represents an improvement of two orders of magnitude in total interferometer phase compared to our earlier CI realization [3]. For these parameters, the maximum separation of interfering states is 1.5mm. The observed δφ=5 mrad at n = 76 (Fig. (b)) then gives a precision of in ω rec in shots. The interferometer cycle time is dominated by the BEC production time. While this is 1 s for this work, we have demonstrated Yb BEC cycle times as low as 1.6 s in our group [3]. Using 3 s as a reasonable benchmark for longterm measurements, the above numbers scale to in ω rec in 1 hrs of integration time. We are () Diffraction Phase (rad) Acceleration pulse Mirror pulse Peak Lattice Depth (recoils) FIG. 4: Diffraction phase shift vs peak lattice depth (with pulse width held fixed) for the second-order Bragg mirror pulse (black circles) and the third-order acceleration pulse (blue diamonds) from k to 8 k. The dashed vertical lines indicate the peak lattice depths at which the π pulse condition is met in each case. Overall phase offsets have been removed to zero the diffraction phase at the π-points. Black and blue solid lines are the predictions from the corresponding numerical model. The dotted orange line is the prediction of the model for the diffraction phase for the third-order Bragg pulse for large n (see text). initiating a new CI configuration with vertically oriented diffraction beams where the limitation on free evolution time is lifted and T = 1 ms (keeping n = 76) is possible in a 7 cm vertical region. The above scaling then indicates a precision of in ω rec in 1 hrs [33]. The corresponding precision in α, which can be determined by combining ω rec and measurements of other fundamental constants [34] is a factor of two better. Together with potential improvements in n and δφ from better diffraction pulse control, this approach holds promise for a 1 1 level measurement of α and QED test [8, 35, 36]. In summary, we have developed a BEC-based highvisibility phase-stable atom interferometer with momentum splitting up to 11 k, which is more than three times larger in momentum separation than earlier realizations with phase-stable free-space interferometers. The robust scalability is acquired from the inherent vibration insensitivity of the interferometer geometry as well as diffraction phase control via our atom optics parameter choices. We demonstrated a quadratic growth of interferometer phase with momentum splitting and a favorable scaling of the performance towards a precision measurement of α. The large momentum splitting interferometers developed in this work can also be adapted towards other applications such as gravity gradiometry [3] and atom interferometer based gravitational wave sensing [1]. Finally, our results also represent an important advance in the use of alkaline-earth-like atoms for precision atom interferometry, where their ground-state magnetic field insensitivity

5 5 and the presence of narrow intercombination transitions can be exploited [3, 37 4]. Jamison for valuable discussions and a critical reading of the manuscript. This work was supported by the National Science Foundation. Acknowledgments We thank Eric Cooper, Brendan Saxberg, and Ryan Weh for important technical contributions, and Alan [1] A. Cronin, J. Schmiedmayer, and D. Pritchard, Rev. Mod. Phys. 81, 151 (9). [] A. Peters, K. Chung, and S. Chu, Metrologia 38, 5 (1). [3] J. McGuirk, G. Foster, J. Fixler, M. Snadden, and M. Kasevich, Phys. Rev. A 65, 3368 (). [4] D. Durfee, Y. Shaham, and M. Kasevich, Phys. Rev. Lett. 97, 481 (6). [5] R. Geiger, V. Mnoret, G. Stern, N. Zahzam, P. Cheinet, B. Battelier, A. Villing, F. Moron, M. Lours, Y. Bidel, et al., Nat. Commun., 474 (11). [6] S. Fray, C. Diez, T. Hnsch, and M. Weitz, Phys. Rev. Lett. 93, 444 (4). [7] D. Schlippert, J. Hartwig, H. Albers, L. Richardson, C. Schubert, A. Roura, W. Schleich, W. Ertmer, and E. Rasel, Phys. Rev. Lett. 11, 3 (14). [8] R. Bouchendira, P. Clade, S. Guellati-Khelifa, F. Nez, and F. Biraben, Phys. Rev. Lett. 16, 881 (11). [9] H. Muller, S. Chiow, S. Herrmann, and S. Chu, Phys. Rev. Lett. 1, 443 (9). [1] S. Chiow, T. Kovachy, H. Chien, and M. A. Kasevich, Phys. Rev. Lett. 17, 1343 (11). [11] We use the term phase-stability to mean that the shot-toshot variation in phase is less than π, i.e. reproducible and therefore usable for a direct interferometric measurement. [1] S. Chiow, S. Herrmann, S. Chu, and H. Muller, Phys. Rev. Lett. 13, 54 (9). [13] H. Muller, S. Chiow, Q. Long, S. Herrmann, and S. Chu, Phys. Rev. Lett. 1, 1845 (8). [14] P. Asenbaum, C. Overstreet, T. Kovachy, D. Brown, J. Hogan, and M. Kasevich, Phys. Rev. Lett. 118, 1836 (17). [15] G. McDonald, C. Kuhn, S. Bennetts, J. Debs, K. Hardman, M. Johnsson, J. Close, and N. Robins, Phys. Rev. A 88, 536 (13). [16] K. Chung, S. Chiow, S. Herrmann, S. Chu, and H. Muller, Phys. Rev. D. 8, 16 (9). [17] P. Altin, M. Johnsson, V. Negnevitsky, G. Dennis, R. Anderson, J. Debs, S. Szigeti, K. Hardman, S. Bennetts, G. McDonald, et al., New J. Phys. 15, 39 (13). [18] A. Sugarbaker, S. Dickerson, J. Hogan, D. Johnson, and M. Kasevich, Phys. Rev. Lett. 111, 113 (13). [19] J. Fixler, G. Foster, J. McGuirk, and M. Kasevich, Science 315, 74 (7). [] G. Rosi, F. Sorrentino, L. Cacciapuoti, M. Prevedelli, and G. Tino, Nature 51, 518 (14). [1] S. Dimopoulos, P. Graham, J. Hogan, M. Kasevich, and S. Rajendran, Phys. Rev. D. 78, 1 (8). [] S. Gupta, K. Dieckmann, Z. Hadzibabic, and D. E. Pritchard, Phys. Rev. Lett. 89, 1441 (). [3] A. O. Jamison, B. Plotkin-Swing, and S. Gupta, Phys. Rev. A 9, 6366 (14). [4] S. Gupta, A. E. Leanhardt, A. D. Cronin, and D. E. Pritchard, Cr. Acad. Sci. IV-Phys, 479 (1). [5] The width of the readout signal is determined by the coherence time 1/k v where v is the velocity spread of the atom source []. The visibility in the central part of the signal is insensitive to the choice of envelope function. We choose a Gaussian shape for convenience. [6] The total number of atoms that contribute to this offset is reduced for higher n because the atomic population not remaining in the intended interferometer paths due to finite diffraction efficiencies eventually leave the area of the readout beam, which is at 44 degrees relative to the diffraction beams. This effect is taken into account in our visibility model. [7] M. Buchner, R. Delhuille, A. Miffre, C. Robilliard, J. Vigue, and C. Champenois, Phys. Rev. A 68, 1367 (3). [8] B. Estey, C. Yu, H. Muller, P. Kuan, and S. Lan, Phys. Rev. Lett. 115, 83 (15). [9] E. Giese, A. Friedrich, S. Abend, E. Rasel, and W. Schleich, Phys. Rev. A. 94, (16). [3] Y. Castin and R. Dum, Phys. Rev. Lett. 77, 5315 (1996). [31] A. O. Jamison, J. N. Kutz, and S. Gupta, Phys. Rev. A. 84, (11). [3] R. Roy, A. Green, R. Bowler, and S. Gupta, Phys. Rev. A. 93, 4343 (16). [33] An analysis of relevant systematic effects for such a measurement can be found in [43]. [34] D. S. Weiss, B. C. Young, and S. Chu, Phys. Rev. Lett. 7, 76 (1993). [35] D. Hanneke, S. Fogwell, and G. Gabrielse, Phys. Rev. Lett. 1, 181 (8). [36] T. Aoyama, M. Hayakawa, T. Kinoshita, and M. Nio, Phys. Rev. Lett. 19, (1). [37] F. Riehle, T. Kisters, A. Witte, J. Helmcke, and C. Borde, Phys. Rev. Lett. 67, 177 (1991). [38] M. Tarallo, T. Mazzoni, N. Poli, X. Zhang, D. Sutyrin, and G. Tino, Phys. Rev. Lett. 113, 35 (14). [39] T. Mazzoni, X. Zhang, R. Del Aguila, L. Salvi, N. Poli, and G. Tino, Phys. Rev. A 9, (15). [4] P. Graham, J. Hogan, M. Kasevich, and S. Rajendran, Phys. Rev. Lett. 11, 1711 (13). [41] J. Hartwig, S. Abend, S. Schubert, D. Schlippert, H. Ahlers, K. Posso-Trujillo, N. Gaaloul, W. Ertmer, and E. Rasel, New J. Phys. 17, 3511 (15). [4] M. Norcia, J. Cline, and J. Thompson, Phys. Rev. A. 96, 4118 (17).

6 [43] A. O. Jamison, University of Washington PhD Thesis (14). 6