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arXiv:cond-mat/0610844

A Cold Atomic Fermi Gas with a Spatially Modulated Interaction

Hao Fu, Alberto G. Rojo

Published Oct 30, 2006• 0 citations
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Abstract

We study an ultra-cold atomic Fermi Gas with the atom-atom interaction modulated periodically in space. A novel ground state with cooper pairs occupying non-zero center of mass momenta is found. Such a state is closely related to the state proposed by Fulde, Ferrell, Larkin, and Ovchinnikov(FFLO). The resultant single particle excitations with momenta along the direction of the modulation shows multiple-gap structures. Such a system can be realized in experiment with a spatially modulated Feshbach resonance. Experimental signatures of such a state are discussed.

DOI
10.48550/arxiv.cond-mat/0610844

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We study an ultra-cold atomic Fermi Gas with the atom-atom interaction modulated periodically in space. A novel ground state with cooper pairs occupying non-zero center of mass momenta is found. Such a state is closely related to the state proposed by Fulde, Ferrell, Larkin, and Ovchinnikov(FFLO). The resultant single particle excitations with momenta along the direction of the modulation shows multiple-gap structures. Such a system can be realized in experiment with a spatially modulated Feshbach resonance. Experimental signatures of such a state are discussed.
We theoretically explore a promising route to achieve the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state in a spin-imbalanced ultracold Fermi gas. In the current stage of cold atom physics, search for this exotic Fermi superfluid is facing two serious difficulties: One is the desperate destruction of the FFLO long-range order by FFLO pairing fluctuations, which precludes entering the phase through a second-order transition, even in three dimension. The other is the fierce competition with the phase separation into the BCS (Bardeen-Cooper-Schrieffer) state and the spin-polarized normal state. By including strong FFLO pairing fluctuations within the framework of the strong-coupling theory developed by Nozi\`eres and Schmitt-Rink, we show that the anisotropy of Fermi surface introduced by an optical lattice makes the FFLO state stable against the paring fluctuations. This stabilized FFLO state is also found to be able to overcome the competition with the phase separation under a certain condition. Since the realization of unconventional Fermi superfluids is one of the most exciting challenges in cold atom physics, our results would contribute to the further development of this field.
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In a very interesting recent Letter\cite{machida}, the authors suggested the possibility of realizing the spatially modulated, or Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) superfluid state in trapped atomic fermion systems. The authors this Letter used a 1D mean field solution as guidance to estimate the parameter range for the existence of the FFLO phase, and also discussed the possibility of its detection by imaging the atomic density of the system. In this comment I wish to make two points. (i) In 1D there exists an exact solution based on bosonization, which fully takes into account the important quantum fluctuation effects\cite{yang01}; the exact solution suggests a wider parameter range for the FFLO state than that obtained from the mean-field solution of the present Letter. (ii) One can detect the FFLO pairing (in which Cooper pairs carry finite momenta) more directly by extending the methods used to detect BCS pairing\cite{regal,altman,greiner}.
The FFLO modulated superconductor state was independently proposed by Fulde and Ferrell, and Larkin and Ovchinnikov, as a way of accommodating the excess spin in a spin-polarized superconductor. The pairs in the FFLO state have non-zero center-of-mass momentum, which can produce a periodic structure with a spatially-modulated order parameter. Although there is some evidence for FFLO pairing in certain heavy fermion compounds that are able to accommodate both magnetic and superconducting order, conclusive experimental proof remains elusive. Motivated by the search for exotic paired states, we have performed experiments with spin-imbalanced ultracold atomic Fermi gases in both 3D and 1D. We use two hyperfine levels of 6Li to emulate the spin-up and down states. The s-wave pairing interactions are controlled via a magnetically-tuned collisional (Feshbach) resonance. In 3D, we find that the gas phase separates into an evenly paired BCS-like core, surrounded by the excess spin-up atoms [1]. For the 1D experiment, a two-dimensional optical lattice was used to create an array of 1D tubes that are each filled with ∼200 atoms. The weak axial confinement again produces a phase separation, but in contrast to 3D we find a partially-polarized central core surrounded by either fully-paired or fully-polarized wings, depending on the degree of overall spin-polarization [2]. Theory predicts that the partially-polarized phase is an FFLO superfluid. We are currently trying to obtain direct evidence for FFLO pairing, which may be revealed in the pair momentum distribution found by releasing the atoms axially and allowing them to expand in time-of-flight. We are also exploring the 1D-3D dimensional crossover that occurs when the coupling between tubes is reduced.
This thesis summarizes work on the theory of many-body effects in atomic systems. The modification of emission rates and spectra for a single impurity atom embedded in a many-body system is studied. In addition, the physics of two, cold atom systems is investigated. We first study the spontaneous decay of a source atom inside a dielectric. In a microscopic picture, the photon radiated by the source atom is scattered by the medium atoms. This scattered photon is absorbed by the source atom, which results in a modification of the atom's decay rate. The calculation is carried out to second order in the medium density and we find a result that differs from the one obtained in macroscopic calculations. Using the same microscopic model, we carry out a microscopic calculation for the recoil momentum acquired by a radiating atom in a medium. In our microscopic calculation, the average value of the photon momentum is modified by its scattering with the source atoms. This gives a modification to the recoil momentum of the source atom. The calculated correction agrees with the experimental observations. In the second part of the thesis, we study two, ultra-cold atomic systems. An exactly solvable model, a Tonks-Girardeau gas with a local potential, is explain first. Such a one dimensional quantum gas has been realized recently. The spectrum of the single particle density matrix is evaluated exactly. We find the "condensate density" as a function of the potential strength. We also propose to use time-of-flight imaging to detect experimental observables. The possibility of modulating the interaction strength in space using a Feshbach resonance in a degenerate Fermi gas is examined in the last part of the thesis. Using a periodic modulation, we find that the ground state of the system contains Cooper pairs with non-zero center-of-mass momenta. The resultant single particle spectrum is found to have an additional gap along particular directions. We propose experimental schemes to detect properties of both the ground state and the quasi-particle excitations.
We propose a two-step experimental protocol to directly engineer Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) states in a cold two-component Fermi gas loaded into a quasi-one-dimensional trap. First, one uses phase imprinting to create a train of domain walls in a superfluid with equal number of $\ensuremath{\uparrow}$- and $\ensuremath{\downarrow}$-spins. Second, one applies a radio-frequency sweep to selectively break Cooper pairs near the domain walls and transfer the $\ensuremath{\uparrow}$-spins to a third spin state, which does not interact with the $\ensuremath{\uparrow}$- and $\ensuremath{\downarrow}$-spins. The resulting FFLO state has exactly one unpaired $\ensuremath{\downarrow}$-spin in each domain wall and is stable for all values of domain-wall separation and interaction strength. We show that the protocol can be implemented with high fidelity at sufficiently strong interactions for a wide range of parameters available in present-day experimental conditions.