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Physical Review A

Coherent population trapping in Raman-pulse atom interferometry

David L. Butts, Joseph M. Kinast, Krish Kotru, Antonije M. Radojevic, Brian P. Timmons, Richard E. Stoner

Published Oct 10, 2011• 8 citations
Publisher

Abstract

Raman pulse atom interferometry is an important modality for precision measurements of inertial forces and tests of fundamental physics. Typical Raman atom optics use two coherent laser fields applied at gigahertz-scale detunings from optical resonance, so that spontaneous emission produces a minor or negligible source of decoherence. An additional consequence of spontaneous emission is coherent population trapping (CPT). We show that CPT produces coherences and population differences which induce systematic effects in Raman pulse atom interferometers. We do not believe that CPT has been previously identified as an error mechanism in Raman pulse atom interferometry. We present an experimental characterization of CPT coherences and population differences induced in laser-cooled cesium atoms by application of Raman pulses at detunings near 1 GHz, commensurate with detunings used in several precision measurement experiments. We are not aware of previous demonstrations of CPT-induced population difference. We argue that CPT effects could induce phase shifts of several milliradians in magnitude for typical experimental parameters and stipulate that these errors can be suppressed by propagation direction reversal in Raman interferometer-based precision measurements.

DOI
10.1103/physreva.84.043613

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Raman pulse atom interferometry is an important modality for precision measurements of inertial forces and tests of fundamental physics. Typical Raman atom optics use two coherent laser fields applied at gigahertz-scale detunings from optical resonance, so that spontaneous emission produces a minor or negligible source of decoherence. An additional consequence of spontaneous emission is coherent population trapping (CPT). We show that CPT produces coherences and population differences which induce systematic effects in Raman pulse atom interferometers. We do not believe that CPT has been previously identified as an error mechanism in Raman pulse atom interferometry. We present an experimental characterization of CPT coherences and population differences induced in laser-cooled cesium atoms by application of Raman pulses at detunings near 1 GHz, commensurate with detunings used in several precision measurement experiments. We are not aware of previous demonstrations of CPT-induced population difference. We argue that CPT effects could induce phase shifts of several milliradians in magnitude for typical experimental parameters and stipulate that these errors can be suppressed by propagation direction reversal in Raman interferometer-based precision measurements.
We investigate the effect of coherent population trapping (CPT) in an atom interferometer gravimeter based on the use of stimulated Raman transitions. We find that CPT leads to significant phase shifts, on the order of a few mrad, which may compromise the accuracy of inertial measurements. We show that this effect is rejected by the kkk-reversal technique, which consists of averaging inertial measurements performed with two opposite orientations of the Raman wave vector kkk, provided that internal states at the input of the interferometer are kept identical for both configurations.
High-precision inertial sensing demonstrations with light pulse atom interferometry have typically used Raman pulses having durations orders of magnitude shorter than the dwell time between interferometer pulses. Environmentally robust sensors operating at high-bandwidth will be required to operate at short (millisecond scale) dwell times between Raman pulses. In such an operational mode, the Raman pulse duration becomes an appreciable fraction of the dwell time between pulses. In addition, high-precision inertial sensing applications have typically been demonstrated in mildly dynamic or nondynamic environments having low rate of change of inertial input, ensuring that applied Raman pulses satisfy the Raman resonance condition. Application of nonresonant pulses will be inevitable in sensors registering time-varying inertial input. We present a diagrammatic technique for calculation of atomic output state populations for multipulse atom optics manipulations that explicitly account for the effects of finite pulse duration and finite Raman detuning effects on the laser-induced atomic phase. We analyze several atom interferometer sequences. We report accelerometer and gyroscope phase evolution for fixed Raman laser frequency difference incorporating corrections in powers of the ratio of pulse duration to time interval between interferometer pulses. Our accelerometer result agrees with other published results.
Coherent-population trapping (CPT) is a multilevel quantum coherence phenomenon of promising applications in atomic clocks and magnetometers. In particular, multipulse CPT Ramsey interferometry is a powerful tool for improving the performance of CPT atomic clocks. Most studies on multipulse CPT Ramsey interferometry consider periodic pulse sequence and time-independent detuning. However, to further improve the accuracy and precision, one may modify the spectrum symmetry which involves a pulse sequence with time-dependent detuning or phase shift. Here we theoretically analyze the multipulse CPT Ramsey interferometry under arbitrary pulse sequences of time-dependent detuning and obtain a general analytical formula. Using our formula, we analyze the popular CPT Ramsey interferometry schemes such as two-pulse symmetric and antisymmetric spectroscopy and multipulse symmetric and antisymmetric spectroscopy. Under periodic pulses, we quantitatively obtain the influences of pulse width, pulse period, pulse number, and Rabi frequency. Furthermore, we examine the impact of CPT pulses and Rabi frequency on the light shift in both two-pulse and multipulse CPT Ramsey interference. Our theoretical results can guide the experimental design to improve the performance of atomic clocks via multipulse CPT Ramsey interferometry.
The use of cold atoms in any sensor operating in a dynamic environment requires that the measurement cycle be conducted before the atom cloud escapes the interaction region. Under multiple-g accelerations it is desirable to complete measurements in millisecond time scales, particularly when laser beams are used to interrogate the atoms. In this paper, we demonstrate high-contrast atom interferometry in a vapor cell using stimulated Raman transitions at millisecond interrogation times. Laser-cooled cesium atoms are interrogated with a sequence of three Raman pulses and the interferometer phase is read out in the same region in which the atoms are trapped. Our system achieved over 70% contrast with a Doppler insensitive interferometer and over 30% contrast with a Doppler sensitive interferometer, in an environment normally considered adverse to high-contrast atom interferometry (e.g., no retroreflector stabilization and no magnetic shielding). Demonstration of an inertially sensitive atom interferometer in this environment supports the feasibility of a high-bandwidth inertial sensor using light pulse atom interferometry. Finally, we show that Raman pulse population transfer efficiency in our system is primarily limited by nonuniformity of the Raman laser intensity across the atom cloud.
The Ramsey method has been applied by means of optical coherent population trapping (CPT) pulses through a cesium vapor cell with N/sub 2/ buffer gas at room temperature, using two phase-locked lasers. With this method, CPT resonance spectral widths are no longer limited by optical saturation and collision effects, but only depend on free evolution time between the two pulses. A fringe width below 100 Hz is reported. Experimental Raman-Ramsey fringes are analyzed using the classical wavefunction formalism.
We report our experiment on sideband cooling with two Raman transitions in a $\mathrm{\ensuremath{\Lambda}}$ configuration that allows selective coherent population trapping (CPT) of the low-lying motional states. The cooling method is applied to 87Rb^{87}\mathrm{Rb}87Rb atoms in a circularly polarized one-dimensional optical lattice. Owing to the vector polarizability, the vibration frequency of a trapped atom depends on its Zeeman quantum number and the CPT resonance for a pair of bound states in the $\mathrm{\ensuremath{\Lambda}}$ configuration depends on their vibrational quantum numbers. We call this scheme motion-selective coherent population trapping (MSCPT) and it is a trapped-atom analog of the velocity-selective CPT developed for free He atoms. We observe a pronounced dip in temperature near a detuning for the Raman beams to satisfy the CPT resonance condition for the motional ground state. Although the lowest temperature we obtain is ten times the recoil limit owing to the heat load from motion along an axis, which is left uncooled, and the large Lamb-Dicke parameter of 2.3 in our apparatus, the experiment demonstrates that MSCPT enhances the effectiveness of Raman sideband cooling and enlarges the range of its application. Discussions of design parameters optimized for MSCPT on 87Rb^{87}\mathrm{Rb}87Rb atoms and opportunities provided by diatomic polar molecules, whose Stark shift shows a strong dependence on the rotational quantum number, are included.