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arXiv:2308.06659 · Physical Review A

Rabi oscillations and magnetization of a mobile spin-1/2 impurity in a Fermi sea

Brendan C. Mulkerin, Jesper Levinsen, Meera M. Parish

Published Feb 1, 2024• 10 citations
arXivHTMLPDF

Abstract

We investigate the behavior of a mobile spin-1/2 impurity atom immersed in a Fermi gas, where the interacting spin-$\ensuremath{\uparrow}$ and noninteracting spin-$\ensuremath{\downarrow}$ states of the impurity are Rabi coupled via an external field. This scenario resembles the classic problem of a two-state system interacting with a dissipative environment, but with an added dimension provided by the impurity momentum degree of freedom. In this case, the impurity can become ``dressed'' by excitations of the Fermi sea to form a Fermi polaron quasiparticle. For the steady-state system, where the impurity has thermalized with the medium, we derive exact thermodynamic relations that connect the impurity magnetization with quasiparticle properties such as the number of fermions in the dressing cloud. We show how the thermodynamic properties evolve with increasing Rabi coupling and we present exact analytical results in the limits of weak and strong Rabi coupling. For the dynamics of the Rabi-driven Fermi polaron, we formulate a theoretical approach based on correlation functions that respects conservation laws and allows the efficient calculation of Rabi oscillations for a range of timescales and impurity momenta beyond what has been achieved previously. Our results are in good agreement with recent experiments on the Rabi oscillations of the attractive polaron, and they reveal how the Rabi oscillations are influenced by the interplay between the polaron and its dressing cloud.

DOI
10.1103/physreva.109.023302

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We investigate the behavior of a mobile spin-1/2 impurity atom immersed in a Fermi gas, where the interacting spin-\ensuremath↑\ensuremath{\uparrow}\ensuremath↑ and noninteracting spin-\ensuremath↓\ensuremath{\downarrow}\ensuremath↓ states of the impurity are Rabi coupled via an external field. This scenario resembles the classic problem of a two-state system interacting with a dissipative environment, but with an added dimension provided by the impurity momentum degree of freedom. In this case, the impurity can become ``dressed'' by excitations of the Fermi sea to form a Fermi polaron quasiparticle. For the steady-state system, where the impurity has thermalized with the medium, we derive exact thermodynamic relations that connect the impurity magnetization with quasiparticle properties such as the number of fermions in the dressing cloud. We show how the thermodynamic properties evolve with increasing Rabi coupling and we present exact analytical results in the limits of weak and strong Rabi coupling. For the dynamics of the Rabi-driven Fermi polaron, we formulate a theoretical approach based on correlation functions that respects conservation laws and allows the efficient calculation of Rabi oscillations for a range of timescales and impurity momenta beyond what has been achieved previously. Our results are in good agreement with recent experiments on the Rabi oscillations of the attractive polaron, and they reveal how the Rabi oscillations are influenced by the interplay between the polaron and its dressing cloud.
We consider a spin impurity with multiple energy levels moving in a noninteracting Fermi sea and theoretically solve this Fermi-spin-polaron problem at nonzero temperature by using a non-self-consistent many-body TTT-matrix theory. We focus on the simplest case with spin 12\frac{1}{2}21​, where the two energy states of the impurity are coupled by a Rabi flip term. At small Rabi coupling, the impurity exhibits damped Rabi oscillations, where the decoherence is caused by the interaction with the Fermi sea, as recently reported in Fermi-polaron experiments with ultracold atoms. We investigate the dependence of Rabi oscillations on the Rabi coupling strength and examine the additional nonlinear damping due to large Rabi coupling. At finite temperature and nonzero impurity concentration, the impurity can acquire a pronounced momentum distribution. We show that the momentum or thermal average can sizably reduce the visibility of Rabi oscillations. We compare our theoretical predictions to recent experimental data and find good agreement without any adjustable parameters.
Quasiparticles are emergent excitations of matter that underlie much of our understanding of quantum many-body systems. Therefore, the prospect of controlling their properties has both fundamental and practical implications. However, in solid-state materials, it is often challenging to understand how quasiparticles are modified by external fields due to their complex interplay with other collective excitations. Here we demonstrate the manipulation of Fermi polarons—quasiparticles formed by impurities interacting with a Fermi gas—in a homogeneous atomic gas using fast radio-frequency control. Exploiting two internal states of the impurity species, we develop a steady-state spectroscopy, from which we extract the energy of the driven polaron. By varying the drive Rabi frequency, we measure the decay rate and the quasiparticle residue of the polaron in the weak-drive limit. At large Rabi frequencies, we observe signs that the drive causes a hybridization of the driven polaron with an incoherent background, leading to the breakdown of a description in terms of textbook quasiparticles. Our experiment establishes the driven Fermi polaron as a promising platform for studying controllable quasiparticles in strongly driven quantum matter and calls for a controlled theoretical framework to describe the dynamics of this strongly interacting quantum system. Fermi polarons are quasiparticles formed by impurities immersed in a Fermi gas. An experiment in an ultracold fermionic gas now shows how to control their properties with a tunable radio-frequency field.
We investigate the metastable repulsive branch of a mobile impurity coupled to a degenerate Fermi gas via short-range interactions. We show that the quasiparticle lifetime of this repulsive Fermi polaron can be experimentally probed by driving Rabi oscillations between weakly and strongly interacting impurity states. Using a time-dependent variational approach, we find that we can accurately model the impurity Rabi oscillations that were recently measured for repulsive Fermi polarons in both two and three dimensions. Crucially, our theoretical description does not include relaxation processes to the lower-lying attractive branch. Thus, the theory-experiment agreement demonstrates that the quasiparticle lifetime is dominated by many-body dephasing within the upper repulsive branch rather than by relaxation from the upper branch itself. Our findings shed light on recent experimental observations of persistent repulsive correlations, and have important consequences for the nature and stability of the strongly repulsive Fermi gas.
We consider the dynamics of an impurity atom immersed in an ideal Fermi gas at zero temperature. We focus on the coherent quantum evolution of the impurity following a quench to strong impurity-fermion interactions, where the interactions are assumed to be short range like in cold-atom experiments. To approximately model the many-body time evolution, we use a truncated basis method, where at most two particle-hole excitations of the Fermi sea are included. When the system is initially noninteracting, we show that our method exactly captures the short-time dynamics following the quench, and we find that the overlap between initial and final states displays a universal nonanalytic dependence on time in this limit. We further demonstrate how our method can be used to compute the impurity spectral function, as well as describe many-body phenomena involving coupled impurity spin states, such as Rabi oscillations in a medium or highly engineered quantum quenches.
The Fermi polaron, formed by an impurity interacting with a surrounding Fermi sea, exemplifies the canonical quasiparticle concept as a cornerstone in our description of quantum many-body systems across a wide range of energy scales. Experiments on atomic quantum gases have provided profound insights into the universal nature of the Fermi polaron. While most previous studies have focused on the case of zero impurity momentum, finite-momentum properties have remained largely uncharted. Here, we investigate the moving Fermi polaron by combining a novel Raman acceleration scheme with high-precision radio-frequency spectroscopy, exploring the quasiparticle dispersion relation over a wide range of momenta. We compare our measurements of energy shifts and spectral linewidths with a microscopic theory and reach quantitative agreement for all momenta. For low momenta, we find the energy of the moving polaron to be fully consistent with the Fermi liquid picture of a dressed particle with a constant effective mass. At high momenta, the polaron approaches the behavior of a weakly interacting bare particle, featuring small energy shifts and weak broadening. For intermediate momenta, broadening is generally larger and, most strikingly, the behavior differs for attractive and repulsive polarons. While the repulsive polaron exhibits a smooth connection between both regimes along with a monotonic change of the energy shift, the attractive case shows a peculiar non-monotonic behavior. With increasing momentum, the attractive polaron enters a regime where its energy deviates from the constant effective mass expression and broadening suddenly increases. By comparing this observation with theory, we show that this abrupt behavior coincides with the attractive polaron entering a molecule-hole continuum, where it is no longer the ground state. We interpret this as a motion-induced polaron-molecule transition.
Motivated by experiments with cold atoms, we investigate a mobile impurity immersed in a Fermi sea in three dimensions at zero temperature by means of the functional renormalization group. We first perform the derivative expansion of the effective action to calculate the ground-state energy and Tan's contact across the polaron-molecule transition for several mass imbalances. Next we study quasiparticle properties of the impurity by using a real-time method recently developed in nuclear physics, which allows one to go beyond the derivative expansion. We obtain the spectral function of the polaron and the effective mass and quasiparticle weight of attractive and repulsive polarons, and clarify how they are affected by mass imbalances.