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arXiv:1703.05877 · Physical Review A

Ultracold atom interferometry with pulses of variable duration

Valentin Ivannikov

Published Mar 16, 2017• 2 citations
arXivHTMLPDF

Abstract

We offer interferometry models for thermal ensembles with one-body losses and the phenomenological inclusion of perturbations covering most of the thermal atom experiments. A possible extension to the many-body case is briefly discussed. The Ramsey pulses are assumed to have variable durations and the detuning during the pulses is distinguished from the detuning during evolution. Consequently, the pulses are not restricted to resonant operation and give more flexibility to optimize the interferometer to particular experimental conditions. On this basis another model is devised in which the contrast loss due to the unequal one-body population decays is canceled by the application of a nonstandard splitting pulse. For the importance of its practical implications, an analogous spin-echo model is also provided. The developed models are suitable for the analysis of atomic clocks and a broad range of sensing applications; they are particularly useful for trapped-atom interferometers.

DOI
10.1103/physreva.95.033621

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We offer interferometry models for thermal ensembles with one-body losses and the phenomenological inclusion of perturbations covering most of the thermal atom experiments. A possible extension to the many-body case is briefly discussed. The Ramsey pulses are assumed to have variable durations and the detuning during the pulses is distinguished from the detuning during evolution. Consequently, the pulses are not restricted to resonant operation and give more flexibility to optimize the interferometer to particular experimental conditions. On this basis another model is devised in which the contrast loss due to the unequal one-body population decays is canceled by the application of a nonstandard splitting pulse. For the importance of its practical implications, an analogous spin-echo model is also provided. The developed models are suitable for the analysis of atomic clocks and a broad range of sensing applications; they are particularly useful for trapped-atom interferometers.
We present a number of analytical means for the analysis of the evolution of an atom clock, emphasizing the role of many-body processes in the population and coherence loss. A master equation with one-body and two-body losses included is presented for a thermal cloud ensemble, suitable for modelling atom clock evolution. Approximate solutions for the coupled rate equations with one-body and two-body losses are obtained for the case of Ramsey free evolution, and their validity is analyzed. An approach is suggested to combine the analytical trap-induced fringe envelope function with a numerically evaluated many-body envelope function. A set of Ramsey and spin echo models is offered with analytical solutions for the off-resonant and on-resonant regimes with one-body population loss and phenomenological dephasing. Their detuning spectra are presented and the difference between them and the standard Ramsey model is shown: the Rabi pedestal in the present model has no spectral ripples due to the pi/2-pulse duration equal to a quarter of a Rabi oscillation, even off resonance, in contrast to the Ramsey method where the pi/2-pulse duration is not corrected off resonance and causes spectral ripples. the off-resonant and on-resonant regimes with one-body population loss and phenomenological dephasing. Their detuning spectra are presented and the difference between them and the standard Ramsey model is shown: the Rabi pedestal in the present model has no spectral ripples due to the pi/2-pulse duration equal to a quarter of a Rabi oscillation, even off resonance, in contrast to the Ramsey method where the pi/2-pulse duration is not corrected off resonance and causes spectral ripples. An interferometric fringe in long evolution experiments is typically measured with a visibility decay primarily due to phase diffusion, phase instability, trapping effects and many-body losses. It constitutes a problem to extract parameters from a fringe obtained in the time domain because of the growing uncertainty of the fringe amplitude and phase. This visibility loss can be compensated for systems with unequal state population losses, as the one we have, by tailoring the pulse durations. Methods are suggested for the one-body and many-body cases.A comprehensive set of experiments is conducted on the characterization of the stability of the trapped atom clock: with condensate and thermal cloud ensembles, with phase-domain Ramsey and spin echo interferometries, with synchronization from a rubidium frequency standard and from an oven-controlled quartz oscillator. The types of noise present in the system are identified by means of an Allan deviation analysis. Despite the 50 times different cloud densities of the condensate and the thermal clouds, an equality of the phase stability in the Ramsey interferometry with BEC and thermal clouds is demonstrated. The spin echo interferometry has shown a slightly superior stability with the thermal clouds as compared to the BEC.
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.
An ensemble density matrix model that includes one- and two-body losses is derived for a trapped-atom clock. A trapped-atom clock is mainly affected by one- and two-body losses, generally giving nonexponential decays of populations; nevertheless, three-body recombination is also quantitatively analyzed to demonstrate the boundaries of its practical relevance. The importance of one-body losses is highlighted without which population trapping behavior would be observed. The model is written with decay constants expressed through experimental parameters. It can complement, e.g., the ISRE (identical spin rotation effect) model to improve its predictions: ISRE dramatically increases the ensemble coherence time, hence it enables one to observe the influence of two-body losses on the interferometry contrast envelope. The presented model is useful for Ramsey interferometry and is ready for immediate experimental verification in existing systems.
Atom interferometric sensors and quantum information processors must maintain coherence while the evolving quantum wave function is split, transformed, and recombined, but suffer from experimental inhomogeneities and uncertainties in the speeds and paths of these operations. Several error-correction techniques have been proposed to isolate the variable of interest. Here we apply composite pulse methods to velocity-sensitive Raman state manipulation in a freely expanding thermal atom cloud. We compare several established pulse sequences, and follow the state evolution within them. The agreement between measurements and simple predictions shows the underlying coherence of the atom ensemble, and the inversion infidelity in a $\ensuremath{\sim}80\phantom{\rule{0.28em}{0ex}}\ensuremath{\mu}\mathrm{K}$ atom cloud is halved. Composite pulse techniques, especially if tailored for atom interferometric applications, should allow greater interferometer areas, larger atomic samples, and longer interaction times, and hence improve the sensitivity of quantum technologies from inertial sensing and clocks to quantum information processors and tests of fundamental physics.
Abstract Ramsey interferometers using internal electronic or nuclear states find wide applications in science and engineering. We develop a matter wave Ramsey interferometer for trapped motional quantum states exploiting the s- and d-bands of an optical lattice and study it both experimentally and theoretically, identifying the different de-phasing and de-coherence mechanisms. Implementing a band echo technique, employing repeated π-pulses we suppress the de-phasing evolution and significantly increase the coherence time of the trapped state interferometer by one order of magnitude. Thermal fluctuations are the main mechanism for the remaining decay of the contrast. Our demonstration of an echo-Ramsey interferometer with trapped quantum states in an optical lattice has potential application in the study of quantum many-body lattice dynamics, and motional qubits manipulation.
Atom interferometry is a highly versatile experimental technique for precision measurement, with applications in inertial sensing and tests of fundamental physics. Such interferometers rely on high fidelity transfer of atoms between internal states, which can be challenging when working with thermal atom clouds, where a range of resonance frequencies exists. Inhomogeneities in the spatial intensity distribution of the manipulation lasers can also give rise to a range of coupling strengths; both of these effects serve to reduce the fidelity of coherent manipulation operations. Composite pulses offer one route to high fidelity coherent manipulations. In this thesis we investigate the performance of composite pulses in a thermal cloud of Rubidium 85. We find remarkable agreement between theory and experimental investigation of composite inversion pulses, and build on this to model the performance of such pulses in atom interferometers. We also find excellent agreement between our model and the first experimental demonstration of an application of interferometry in the cooling of atoms; this is the first step towards implementing this cooling method in complex structures like molecules.