Atom interferometry in a moving guide

Transcription

1 Atom interferometry in a moving guide Saijun Wu 1,2, Edward J. Su 1, Mara Prentiss 1 1. Department of Physics and Center for Ultra Cold atoms, Harvard University, Cambridge, MA, Division of Engineering and Applied Science, Harvard University, Cambridge, MA, PACS: be, t, Vk Abstract: We demonstrate a current-controlled magnetic guide that can transport atoms in the direction perpendicular to the waveguide. We have combined this with a light pulse Talbot-Lau interferometer that splits and recombines atom wavepackets along the free propagation direction of the waveguide, resulting in an interferometric path that encloses area and thus can be used to sense rotation.

2 Rotation sensing has always been one of the most important proposed applications of atom interferometry because, as was pointed out by Clauser [1] almost thirty years ago, the phase shift due to rotation for an atom interferometer is more than 10 9 times larger than the phase shift/rotation of a photon interferometer that encloses the same area; however, the phase shift is proportional to area and the area enclosed by atom interferometers have been significantly smaller than those enclosed by photon interferometers. Free space atomic gyroscopes are typically limited by small beam splitting angles, so long lengths (~ 2 m) are required in order to achieve significant enclosed areas (~ 22 mm 2 ) [2, 3]. Guided atom interferometers have attracted lots of attentions since atom guides can send atoms around square or circular paths with enclosed areas that can be much larger than the areas enclosed in free space [4-9], while remaining compact. Atoms have been guided around paths that enclose areas up to 10 cm 2 on centimeter-scale devices [6-9]; however, it has not been demonstrated that external state atomic coherences are preserved as the atoms propagated around these guide loops. It has recently been shown that atom wavepackets confined in straight magnetic waveguides can be split and recombined to produce an atom interference signal that has a reproducible phase, but in these experiments no physical area is enclosed in the interference pathways. [10-12]; consequently, these interferometers cannot measure rotation. In this paper, we demonstrate a waveguide based atom interferometer that encloses area and could be used for rotation sensing. Guided photon rotation sensors use

3 waveguide beamspsitters to separate and recombine the guided light beams, so many proposed guided atom interferometers also use the guiding potentials to split and recombine the atoms [13-15]. Compare with photons, response of atoms to the guiding potential is more dispersive (e.g., energy dependent), and beam splitting with guiding potentials has proved to be very challenging, particularly if widely separated outputs are desired. [16]. In this paper we propose an alternate technique: while the magnetic guide transports the guided atoms along its transverse directions, the splitting and recombining of the matterwaves are realized instead by standing wave pulses acting along the free propagation direction of the guide, (fig.1). This combination of optical beam splitting and magnetic guiding has already been shown to preserve phase when the magnetic guide is stationary and no area is enclosed.[10-12] In this paper we demonstrate that phase is still preserved when the waveguide is translated, so that the interferometric paths enclose area and rotation sensing should be possible. This experiment differs from various atom-chip based experiments with Bose-Einstein condensates as the atom sample here is thermal and is distributed over thousands of waveguide modes. This allows us to treat the transverse motion of atoms classically. In addition, the density in the sample is sufficiently low that we can safely neglect effects of inter-atomic collisions for interrogation times less than a second. To avoid altering the internal states of the magnetically confined atoms, we use off-resonant standing wave light pulses to diffract the atoms confined in the magnetic guide via the light shift potential. The pulse durations are chosen to be 300nanoseconds,

4 which is short enough that the atomic kinetic energy of the 20 μ K atomic sample can be ignored during the pulse durations. In this so-called Raman-Nath region, single atoms undergo n th order diffraction acquire 2n photon recoil momentum is with a diffraction amplitude of i (θ ). Here J (θ ) is the n th order Bessel function. The pulse n J n n area θ Ω dτ AC is defined as the integrated light shift during the light pulse. In this experiment θ is chosen to be around 3~4. The atom loss due to each standing wave pulse is less than 10% of trapped atoms, where the loss is probably due to spontaneous emission and spin flips. The atom interferometer follows the 3-pulse Talbot-Lau interferometry scheme [17, 18]. In particular, two standing wave pulses at time 0 and T/2 are applied to diffract atoms to multiple diffraction orders. Diffraction orders that differ by 2 photon recoils are expected to interfere around the echo time T to form an atomic density grating. This atom density grating has the same spatial periodicity as the standing wave to be half the light wavelength. The density grating can thus be probed by monitoring the backscattering of one traveling laser to the other direction. Due to the quantized recoil energy difference between the diffraction orders, the amplitude of the atomic density grating is a periodic function of the total interrogation time T, and is given by [17, 18]: ρ Q T i T ( Qut / 2) 4 ( T + t) ρ θ 1 tj 2[2θ 2Sin( Q )] e e (1) 2m 2 Q a Here Q is the standing wave k-vector. ρ is the atomic density. θ 1, 2 are the pulse are for the 1 st and the 2 nd standing wave pulses. and m are the Plank constant and the mass of the atom, u is the

5 thermal velocity of the atoms. a is the acceleration constant along the standing wave direction, which can be due to the Coriolis force in a rotating frame if the interfering orders form a loop that enclose an area. Our experimental setup is an upgrade based on that described in [11]. We use four soft ferromagnetic ( μ -metal) foils (200mm by 100mm by 1.5mm), separated by distances of 6.35mm, 12.7mm and 6.35mm, magnetized in alternative directions with current-carrying wires to generate a 2Dimensional magnetic quadruple field 7 mm away from the plane defined by four parallel edges of the 4-foils. The 4-foil structure is mounted on two rotation stages close to a vacuum glasscell, inside which laser cooled Rb 87 atoms are trapped at the center section of quadruple line (See fig. 2). Aligned along the guide direction is an off-resonant standing wave field composed of two nearly counter-propagating traveling laser beams, each with 0.9mm 1/e 2 beam diameters, which will be referred to as traveling light mode E TF and E TB in following discussions. The standing wave is 120 MHz blue detuned to F=1 F =2 transition of Rb 87 atoms. In the experiment, around 10 7 laser-cooled Rb 87 atoms are loaded to the magnetic guide with a transverse gradient of 70Gauss/cm, end up with a cylindrically shaped trapped atom sample of 1cm long and 150 μ m wide. The atoms in the magnetic guide can be precisely positioned across the standing wave region by tuning the currents running through the wires that are wound around the two inner foils (Fig.2). The 3-pulse interferometer sequence is launched 30milliseconds after the atoms are loaded into the magnetic guide. The backscattering of E TF around the echo time of the Talbot-Lau

6 interferometer is collected via an avalanche photodiode through a single-mode fiber which is pre-aligned with E TB mode. A weak local field from E TB is frequency shifted and beat against the backscattered light to retrieve its phase information that reflects the relative distance between the nodes of the standing wave and the atom density grating. The experimental sequence is repeated every 3 seconds. Precise alignment of the magnetic guide direction relative to the standing wave direction is achieved by adjusting the 4-foil structure with two rotation stages to optimize the interferometer signals at large interrogation time T [19]. In fig. 3 we summarize typical readouts of the 3-pulse Talbot-Lau interferometer at different time scales. The dispersive-shaped curve (fig 3a) of the backscattering light amplitude reflects the self-re-imagine of the density grating immediately after the first pulse (fig 1), in agreement with equation (1). The oscillatory dependence of the amplitude of the backscattering amplitude (the interferometer contrast) on the total interrogation time T matches equation (1) nicely (fig3b) if a small imaginary component of the pulse area is included to account for the atom loss [11]. The long-term evolution of the contrast oscillations can be investigated by sampling the envelope of the oscillations. With the direction of the guide and the standing wave aligned to a precision better than quarter a milli-radian, the interferometric interrogation time for guided atoms is extended to more than 35ms (fig3c)., as compared with 15ms transient time of atoms escape the standing wave region in free space [20]. The interferometer has a phase readout quadratically depends on the interrogation time, This is due to the phase shift of the atomic coherence

7 by a 0.8% gravity component along the standing wave and thus the guide direction (fig3d) [20]. The interferometer paths enclose an area, when we shift the atomic sample position by translating the waveguide during the three-pulse interferometer sequence. The translating speed is limited by the finite response time of the 4-foil magnetic structure, and also by the finite confining potential of the magnetic guide. We use a guide potential with a 70G/cm transverse gradient. Depending on the moving direction, a one-way linear ramp of currents around the inner foil pairs can move atoms with a uniform velocity of mm/s without significant heating. The maximum translation is limited by the cross section of the standing wave. With our interferometer arrangement, we found the 1mm 1/e 2 diameter of the standing wave cross section can support a 0.5mm translation distance. We prepare the atomic sample at one side of the standing wave region and translate the magnetic guide to the other side, choosing a translating speed of v guide =18mm/sec so that this 0.5mm distance of translation is completed in 28ms. The 1 st, 2 nd, and the detecting pulses of the 3-pulse interferometer are launched at 0, T/2 and around T, with T scanned from 0 up to 35ms in repeated experiment. The diffraction pathways that contribute to the backscattering signal at the interrogation time T enclose an area of 1 1 A( T ) T = d( T ) vrt vguidevr (0<T<28ms). Here d(t) is the transverse displacement of the atomic sample during the interrogation time T. v r = 5.9mm/s is the recoil velocity of Rb 87. Fig.4 gives typically interferometer readouts with atoms in such moving guides. In

8 this measurement the atoms are transported vertically (fig 4a) either upward or downward. The standing wave intensity variation is about 50% of its maxim across the 0.5mm atomic sample trajectory. The phase (e.g., the position of the standing wave nodes) variation of the standing wave along the atom sample trajectory is estimated to be less than 0.2 radiant. The interferometer backscattering signal amplitude as a function of T is plotted in fig4a for both upward and downward experiment. Compare with the contrast decay data for the stationary guide as shown in fig3c, in the moving guide case the contrast decay is first delayed and then accelerated, as expected due to the time-dependent overlap between the atomic sample and the standing wave. Same as the stationary guide case, here the quadratic phase shifts of the interferometer readout are due to the 0.8% gravity component along the guide, and are nearly identical for the upward and downward moving guide case. The difference of the phase readouts from the two moving guide (fig4c) is due to long term drift of the air-floated optical table that changes the tilting angle of the guide relative to gravity. In this experiment the interferometer path covers an area of 0.04mm 2. With the phase resolution of 0.8 radiant at T=28ms, the interferometer can resolve rotation rate on the order of a milli-herz perpendicular to the area. The phase noise in our interferometer system is largely due to mirror vibrations, which is verified by comparing (fig. 3d) the noise in the atom interferometer with the time-dependent phase correlations between the two traveling laser calculated with the beat notes from an optical interferometer that shares the same optics with the atom interferometer system. In addition, unwanted light

9 scatterings off the optics degrade the signal to noise ratio of the interferometer at small interferometer contrast and thus the phase readout. The phase noise should be greatly suppressed with active mirror vibration compensations. The signal to noise ratio can be improved by employing truly white interferometer schemes such as those using Bragg splitting scheme [21] or more recently developed double-pulse interferometer scheme [10, 22]. The area enclosed in the interferometer is limited by the interrogation time, the guide moving speed, and in this experiment the 0.5mm diameter of the standing wave field cross-section. In this experiment, the 35ms interrogation time is limited by the dephasing due to inhomogeneity of the magnetic confining field along the guide across the 1cm atomic sample [19]. To overcome this, we need the atomic sample to be colder and more localized along the guide. To increase the transportation distance, we plan to use a standing wave field with elliptical cross section that allows the atoms to move along its long axis. Due to the big inductance of the magnetic structures and not-so-tight confinement, we haven t been able to move atoms in round trips in between the light pulses without spreading them out, though we believe it is possible with straightforward improvement of the magnetic field control. In conclusion, we have demonstrated a current-controlled moving magnetic guide that transports atoms transversely during a 3 - light pulse atom interferometer sequence along the guide. We have found encouraging decoupling of the degree of freedoms for the interferometer and for the transverse control, and achieve an interferometer path that

10 enclose an area of 0.04mm 2. The demonstrated guided atom interferometer with foreseeable improvements may allow a 100ms interrogation time with 2cm translation distance. When combined with multi-photon beam splitting technique [22], this would allow an interferometer path include an area beyond 10mm 2. The scheme discussed in this paper may be developed to a rotation sensing device featured with compact interference paths and long interrogation time. This work is supported by MURI and DARPA from DOD, NSF, ONR and U.S. Department of the Army, Agreement Number W911NF , and by Draper Lab. Reference [1] Clauser, Ultra-high sensitivity accelerometers and gyroscopes using neutral atom matter-wave interferometry, Physica B 151 (1988) 262 [2] Gustavson TL, Bouyer P, Kasevich MA, Precision rotation measurements with an atom interferometer gyroscope, PHYSICAL REVIEW LETTERS 78 (11): MAR [3] Gustavson TL, Landragin A, Kasevich MA, Rotation sensing with a dual atom-interferometer Sagnac gyroscope, Classical and Quantum Gravity, 17, 2385, 2000 [4] Dumke R, Muther T, Volk M, et al. Interferometer-type structures for guided atoms PHYSICAL REVIEW LETTERS 89 (22): Art. No NOV [5] Vengalattore M, Prentiss M, A reciprocal magnetic trap for neutral atoms, EUROPEAN PHYSICAL JOURNAL D 35 (1): AUG 2005

11 [6] Sauer JA, Barrett MD, Chapman MS, Storage Ring for Neutral atoms, Physical Review Letters, 87(27) , 2001 [7] Wu et al, Bidirectional propagation of cold atoms in a "stadium"-shaped magnetic guide PHYSICAL REVIEW A 70 (1): Art. No JUL 2004 [8] Gupta S, Murch KW, Moore KL, Purdy TP, Stamper-Kurn DM, Bose-Einstein condensation in a circular waveguide, PHYSICAL REVIEW LETTERS 95 (14): Art. No SEP [9] Arnold AS, Garvie CS, Riis E, Large magnetic storage ring for Bose-Einstein condensates, PHYSICAL REVIEW A 73 (4): Art. No APR 2006 [10]Wang YJ, et al, Atom Michelson interferometer on a chip using a Bose-Einstein condensate, PHYSICAL REVIEW LETTERS 94 (9): Art. No MAR [11] Wu S, Su EJ, Prentiss M, Time domain de Broglie wave interferometry along a magnetic guide, EUROPEAN PHYSICAL JOURNAL D 35 (1): AUG 2005 [12] Garcia, et al, Cond-matt/ [13] ANDERSSON E et al, Multimode interferometer for guided matter waves, PHYSICAL REVIEW LETTERS 88, Art. No [14] Das KK, Girardeau MD, Wright EM, Interference of a thermal Tonks gas on a ring, PHYSICAL REVIEW LETTERS 89 (17): Art. No OCT [15] Hansel W, Reichel J, Hommelhoff P, Hansch TW, Trapped-atom interferometer in a magnetic microtrap, Physical Review A, 64, , 2001

12 [16] Schumm T, Hofferberth S, Andersson LM, et al. Matter-wave interferometry in a double well on an atom chip, NATURE PHYSICS 1 (1): OCT 2005 [17] S.B. Cahn et al, Time Domain De Broglie Wave interferometry, Physical Review Letters, 79, 784, (1997) [18] D. V. Strekalov, Andrey Turlapov, A. Kumarakrishnan, and Tycho Sleator, Periodic structures generated in a cloud of cold atoms, PHYSICAL REVIEW A 66, , 2002 [19] Su EJ, et al, in preparations [20] We recently demonstrated a coherence time of 0.7 seconds in a modified light-pulse interferometer scheme with guided atoms. To be published. [21] Giltner, DM, McGowan, RW, Lee, SA, Atom interferometer based on Bragg scattering from standing light waves, Physical Review Letters, 75, 2638,1995 [22] Wu, S., Wang, Y. J., Diot, Q. Prentiss, M. Splitting matter waves using an optimized standing-wave light-pulse sequence. Phys. Rev. A 71,

13 t=0 t=t/2 t=t E l, Local field (Frequency shifted) E TB v guide v guide v guide In phase Out of phase Es T/us E TF x D Ep, probe Demodulation Scope z RF LO Fig. 1 Schematic of the experiment in this work. The three blue bars represent the magnetic guide that moves from left to right along the z axis. The red arrows indicate the pulsed standing wave at different time/positions. Atomic density evolution along the guide during the process is simulated and plotted using a density plot. A loop in green is added to the plot to indicate a wavepacket pathway that contributes to the signal. On the right is a representative signal retrieved in the experiment. All the carton figures are not in proportion to the actual scales.

14 I outer2 1mm (c) (a) I inner2 I inner1 /Amp B I inner1 I outer1 4 I inner2 /Amp g I outer1 =I outer2 =3.5Amp, B 1 ~70G/cm z y (b) Fig. 2. Positioning the atom guide. a) Cross-section of the 4-foil structure along its 20cm long-axis. The current-carrying wires around the foils are also indicated. On the left is a contour plot of the magnetic field distribution. (b) The magnetic structure is mounted close the vacuum cell on two rotation stages (c) Absorption images of the atomic sample across the standing wave region positioned by the magnetic guide. The gravity has a 0.8% component perpendicular to the graph pointing inside. All the carton figures are not in proportion to the actual scales.

15 Es (a) In phase Out of phase Amplitude (b) T/us T/us Phase/Radian Residual/Radian 3 0 a=75.40+/-0.01mm/s (d) T/us Contrasu/au 8 4 envelope 70G/cm (c) T/us Fig. 3 The Talbot-Lau interferometry data. (a) Single experiment back-scattering signal, same as shown in fig.1 (b) amplitude of the backscattering signal shows recoil oscillations. Red line is a fit to theory based on experimental parameters. (c) Sampling the peak points in each recoil oscillations in (b) gives long term behavior of interferometry contrast decay. (d) The optical phase retrieved by comparing the real and imaginary part of the curve in (a). Here the parabolic phase is due to a small component of gravity along the guide. Inset is the phase residual; the red line is the expected noise level due to mirror vibrations.

16 Contrast/au (a) (b) Red: 0.5mm up in 28ms Blue: 0.5mm down in 28ms T/us Phase/Radian R^2 = a1=77.88+/-0.02mm/s^2 a2=77.96+/-0.02mm/s^ T/us t/ms (c) 1mm Differential Phase/Radian 3 0 z y T/us g (d) Fig. 4 Interferometer signals with atoms in a moving guide. Top: A series of absorption images along the magnetic guide that moves up (top) and down (bottom) in 28ms. Two dashed arrows along the trajectories of the atomic sample are drawn to guide eyes.. The gravity has a 0.8% component perpendicular to the graph pointing inside. Bottom: Interferometer signal with interrogation time T from 0 to 35ms. (a) The Contrast decay for the interferometer sequence with atoms in a guide moving up (red) and down (blue). (b) The upward and downward interferometer phase readout. (c) The difference of the retrieved phases for atoms in the guide moving up and down.