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arXiv:1306.2947 · Physical Review Letters

Dissipative Dynamics of a Driven Quantum Spin Coupled to a Bath of Ultracold Fermions

Michael Knap, Dmitry A. Abanin, Eugene Demler

Published Dec 27, 2013• 23 citations
arXivHTMLPDF

Abstract

We explore the dynamics and the steady state of a driven quantum spin coupled to a bath of fermions, which can be realized with a strongly imbalanced mixture of ultracold atoms using currently available experimental tools. Radio-frequency driving can be used to induce tunneling between the spin states. The Rabi oscillations are modified due to the coupling of the quantum spin to the environment, which causes frequency renormalization and damping. The spin-bath coupling can be widely tuned by adjusting the scattering length through a Feshbach resonance. When the scattering potential creates a bound state, by tuning the driving frequency it is possible to populate either the ground state, in which the bound state is filled, or a metastable state in which the bound state is empty. In the latter case, we predict an emergent inversion of the steady-state magnetization. Our work shows that different regimes of dissipative dynamics can be explored with a quantum spin coupled to a bath of ultracold fermions.

DOI
10.1103/physrevlett.111.265302

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We explore the dynamics and the steady state of a driven quantum spin coupled to a bath of fermions, which can be realized with a strongly imbalanced mixture of ultracold atoms using currently available experimental tools. Radio-frequency driving can be used to induce tunneling between the spin states. The Rabi oscillations are modified due to the coupling of the quantum spin to the environment, which causes frequency renormalization and damping. The spin-bath coupling can be widely tuned by adjusting the scattering length through a Feshbach resonance. When the scattering potential creates a bound state, by tuning the driving frequency it is possible to populate either the ground state, in which the bound state is filled, or a metastable state in which the bound state is empty. In the latter case, we predict an emergent inversion of the steady-state magnetization. Our work shows that different regimes of dissipative dynamics can be explored with a quantum spin coupled to a bath of ultracold fermions.
We study the behavior of the Rabi oscillations of a driven central spin (qubit) coupled to an antiferromagnetic spin bath (environment). It is found that the decoherence behavior of the central spin depends on the detuning, driving strength, qubit–bath coupling and an important factor Ω, associated with the number of coupled atoms, the detailed lattice structure and the temperature of the environment. If detuning exists, Rabi oscillations may show the behavior of collapses and revivals; however, if detuning is absent, such a behavior will not appear. We investigate the weighted frequency distribution of the time evolution of the central spin inversion and give a reasonable explanation of this phenomenon of collapses and revivals. We also discuss the decoherence and pointer states of the qubit from the perspective of von Neumann entropy. We found that the eigenstates of the qubit self-Hamiltonian emerge as pointer states in the weak system–environment coupling limit.
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 derive dynamical equations for a driven, dissipative quantum system in which the environment-induced relaxation rate is comparable to the Rabi frequency, avoiding assumptions on the frequency dependence of the environmental coupling. When the environmental coupling varies significantly on the scale of the Rabi frequency, secular or rotating wave approximations break down. We avoid these approximations, yielding dynamical steady states which account for the interaction between driven quantum dots and their phonon environment. The theory, which is motivated by recent experimental observations, qualitatively and quantitatively describes the transition from asymmetric unsaturated resonances at weak driving to population inversion at strong driving.
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In this thesis we investigate the interplay between dissipation and driving in nonlinear quantum systems for a special setup: a flux qubit read out by a DC-SQUID - a nonlinear quantum oscillator. The latter is embedded in a harmonic bath, thereby mediating dissipation to the qubit. Two different approaches are elaborated: First we consider a composite qubit-SQUID system and add the bath afterwards. We derive analytical expressions for its eigenstates beyond rotating wave approximation (RWA), by applying Van Vleck perturbation theory (VVPT) in the qubit-oscillator coupling. The second approach is an effective bath approach based on a mapping procedure, where SQUID and bath form an effective bath seen by the qubit. Here the qubit dynamics is obtained by applying standard procedures established for the spin-boson problem. This approach requires the knowledge of the steady-state response of the dissipative Duffing oscillator, which is studied within a resonant and an off-resonant approach: The first is applicable near and at an N-photon resonance using VVPT beyond a RWA. The second is based on the exact Floquet states of the nonlinear driven oscillator. The dissipative qubit dynamics is described analytically for weak system-bath coupling and agrees well for both approaches. We derive the effect of the nonlinearity on the qubit dynamics, on the Bloch-Siegert shift and on the vacuum Rabi splitting.
We investigate the response to radio-frequency driving of an ultracold gas of attractively interacting fermions in a one-dimensional optical lattice. We study the system dynamics by monitoring the driving-induced population transfer to a third state, and the evolution of the momentum density and pair distributions. Depending on the frequency of the radio-frequency field, two different dynamical regimes emerge when considering the evolution of the third-level population. One regime exhibits (off-)resonant many-body oscillations reminiscent of Rabi oscillations in a discrete two-level system, while the other displays a strong linear rise. Within this second regime, we connect, via linear response theory, the extracted transfer rate to the system single-particle spectral function and infer the nature of the excitations from Bethe ansatz calculations. In addition, we show that this radio-frequency technique can be employed to gain insights into this many-body system coupling mechanism away from equilibrium. This is done by monitoring the momentum density redistributions and the evolution of the pair correlations during the drive. Capturing such nonequilibrium physics goes beyond a linear response treatment and is achieved here by conducting time-dependent matrix-product-state simulations.