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arXiv:0804.3842 · Physical Review A

Adiabatic Rosen-Zener interferometry with ultracold atoms

Libin Fu, Difa Ye, Chaohong Lee, Weiping Zhang, Jie Liu

Published Jul 29, 2009• 19 citations
arXivHTMLPDF

Abstract

We propose a time-domain ``interferometer'' based on double-well ultracold atoms through a so-called adiabatic Rosen-Zener process, that is, the barrier between two wells is ramped down slowly, held for a while, and then ramped back. After the adiabatic Rosen-Zener process, we count the particle population in each well. We find that the final occupation probability shows nice interference fringes. The fringe pattern is sensitive to the initial state as well as the intrinsic parameters of the system such as interatomic interaction or energy bias between two wells. The underlying mechanism is revealed and possible applications are discussed.

DOI
10.1103/physreva.80.013619

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Cambridge University Press eBooks•Jul 23, 2021•0 citations
We propose a time-domain ``interferometer'' based on double-well ultracold atoms through a so-called adiabatic Rosen-Zener process, that is, the barrier between two wells is ramped down slowly, held for a while, and then ramped back. After the adiabatic Rosen-Zener process, we count the particle population in each well. We find that the final occupation probability shows nice interference fringes. The fringe pattern is sensitive to the initial state as well as the intrinsic parameters of the system such as interatomic interaction or energy bias between two wells. The underlying mechanism is revealed and possible applications are discussed.
We investigate the Rosen-Zener-St\"uckelberg interferometry of ultracold atoms in a sinusoidal-type periodical modulated, symmetrical double-well potential. Periodical modulation of the trapping potential barrier leads to an analog of light-assisted Rosen-Zener tunneling, with distinct signatures of the energy gap visible in the amount of particles transferred from one well to the other. Time-averaged atomic occupations in one well show nice interference patterns for multiple-period modulation. The condition for constructive interference is given by the requirements satisfied by the St\"uckelberg phase. Both integer and noninteger resonances ranging from 2n2n2n to 5n5n5n (nnn is a positive integer) are predicted at certain modulating amplitudes. In particular, we find that the resonance profiles can change from a Fano-like line shape with weak modulation to a Lorentzian-like line shape with strong modulation. Our theory is generic for many other forms of periodical modulation fields and can be used to realize a time-domain multiple-slit interferometer.
We propose a feasible scheme to realize nonlinear Ramsey interferometry with a two-component Bose-Einstein condensate, where the nonlinearity arises from the interaction between coherent atoms. In our scheme, two Rosen-Zener pulses are separated by an intermediate holding period of variable duration and through varying the holding period we have observed nice Ramsey interference patterns in the time domain. In contrast to the standard Ramsey fringes our nonlinear Ramsey patterns display diversiform structures ascribed to the interplay of the nonlinearity and asymmetry. In particular, we find that the frequency of the nonlinear Ramsey fringes exactly reflects the strength of nonlinearity as well as the asymmetry of system. Our finding suggests a potential application of the nonlinear Ramsey interferometry in calibrating the atomic parameters such as scattering length and energy spectrum.
We adopt a nonlinear two-mode model to investigate the Rosen-Zener-St\"uckelberg (RZS) interferometry of an interacting Bose-Einstein condensate trapped in double-well potential with a periodically modulating barrier. For symmetric potential, we analyze the properties of interference patterns and derive the interference conditions. For asymmetric potential, we explore the resonance structures caused by destructive interference at the weakly coupling limit and obtain the resonance conditions. In particular, we find that the chaotic motions in the asymmetric case with low-frequency modulation, can destroy the formation of interference fringes. In the symmetric case with high-frequency modulation, we see Fano-line-like resonance structures and find that the reso- nance positions exactly correspond to the boundary of macroscopic quantum self-trapping. We show that the nonlinearity can significantly alter both the shape and position of interference fringes and resonance structures. We discuss the experimental feasibility by comparing the solution of the Gross-Pitaevskii equation with both the solution of the two-mode model and the truncated Wigner simulation as well. The results suggest important applications of nonlinear RZS interferometry both in precisely controlling the dynamics and in accurately measuring the parameters of interacting many-body systems.
Taking Rosen-Zener tunneling as the underlying process，a scheme to achieve nonlinear Ramsey interferometry with a two-component trapped Bose-Einstein condensate is proposed. Abundant nonlinear Ramsey interference fringes are observed in time domain by the numerical simulations and these fringes are very different from the sinusoidal pattern for linear Ramsey interference due to the dominant nonlinear interaction between atoms. Furthermore，Fourier transformation results show that the fundamental frequency of Ramsey fringes can exactly reflect the information of nonlinearity or asymmetry. This finding provides an opportunity to measure atomic properties via measuring the frequency of fringes.
Abstract Ultracold gases provide an excellent platform for the realization of quantum interferometers. In the case of implementations based on Bose-Einstein condensates in double well potentials, an effective two-mode model allows to study how the interactions among particles affect the sensitivity of the interferometer. In this work we review the properties of such a model and its application to interferometric protocols, focusing on the achievable sensitivity in the presence of interactions turned on. In particular we study the full interferometric sequence when the initial state is a Twin Fock state, which is perfectly number squeezed. We found that in the presence of interactions and for certain values of the holding time in which a phase difference between the two modes is accumulated, the same sensitivity as in the non interacting case is recovered when using the population imbalance between the two wells as observable. Finally, we characterize the behaviour of the sensitivity by looking at the δ-derivative and the variance of the operator used for the measurement and studying the squeezing parameters.
This chapter describes the Bose--Einstein condensate (BEC) interferometry. We first introduce the optical interferometer, briefly discussing the role of fringe contrast in observing interference patterns. Next, we examine a BEC interferometer in a Michelson geometry that consists of a BEC in a trapping potential well. The BEC cloud in the potential well is put into a linear superposition of two clouds that travel along different paths in the trap and are recombined using the same light beams. By studying the population of atoms in the different motional states of the BEC clouds that emerge after recombination, we obtain information about the relative phase shift accumulated by the two traveling superposed condensates during the interferometry. We then characterize the atom distribution that is found in the output of the interferometer by finding the probability density distribution and calculating the features of the probability density such as the mean, the variance, and the interference fringe contrast. Finally, we parameterize the effect of two-body collisional interactions on the observed interference fringes in a way that can be directly controlled in an experiment.