We show that the steady state of a periodically driven Bose gas coupled to a thermal bath features emergent Fermi surfaces both in its high temperature and Bose-Einstein-condensate (BEC) states. These emergent Fermi surfaces are non-analyticities in the occupation function as a function of momentum arising from the lack of detailed balance of collisions away from equilibrium. They are stronger in the BEC than in the normal gas, and can be more robust against finite temperature smearing than the usual equilibrium Fermi surfaces of Fermi gases. We also show that they give rise to analogous rich phenomena, such as Friedel oscillations in the density correlations and quantum oscillations in response to applied magnetic fields controlled by their areas, albeit with marked quantitative differences. Our results establish non-equilibrium conditions as a promising alternative pathway to achieve the long-sought-after emergence of Fermi surfaces in bosonic system. We outline strategies to experimentally discover these exotic states in ultra-cold atomic clouds.
We show that the steady state of a periodically driven Bose gas coupled to a thermal bath features emergent Fermi surfaces both in its high temperature and Bose-Einstein-condensate (BEC) states. These emergent Fermi surfaces are non-analyticities in the occupation function as a function of momentum arising from the lack of detailed balance of collisions away from equilibrium. They are stronger in the BEC than in the normal gas, and can be more robust against finite temperature smearing than the usual equilibrium Fermi surfaces of Fermi gases. We also show that they give rise to analogous rich phenomena, such as Friedel oscillations in the density correlations and quantum oscillations in response to applied magnetic fields controlled by their areas, albeit with marked quantitative differences. Our results establish non-equilibrium conditions as a promising alternative pathway to achieve the long-sought-after emergence of Fermi surfaces in bosonic system. We outline strategies to experimentally discover these exotic states in ultra-cold atomic clouds.
A periodically driven Fermi gas coupled to a simple boson bath reaches a non-equilibrium steady-state occupation with sharp non-analyticities at certain momenta. Here, we demonstrate that these non-analyticities behave as emergent Fermi surfaces by showing that they give rise to quantum oscillations of observables with a period controlled by the effective Fermi surface area enclosed by these non-analyticities. However, these oscillations have several striking differences with standard equilibrium quantum oscillations. For example, they remain non-analytic at finite temperatures, their amplitude can survive up to extremely high temperatures comparable to the frequency of the drive, and they can display non-monotonic temperature dependence completely at odds with standard Lifshits-Kosevich behavior.
We demonstrate that periodically driven Fermions coupled to simple bosonic baths have steady state occupations of Floquet Bloch bands that generically display nonanalyticities at certain momenta that resemble the Fermi surfaces of equilibrium non-Fermi liquids. Remarkably these nonequilibrium Fermi surfaces remain sharp even when the bath is at finite temperature, leading to critical power-law decaying correlations at finite temperature, a phenomenon with no analog in equilibrium. We also show that generically there is in-gap current rectification for clean metals lacking inversion symmetry, and explain why this occurs universally regardless of the details of collisions.
We investigate nonequilibrium steady states of driven-dissipative ideal quantum gases of both bosons and fermions. We focus on systems of sharp particle number that are driven out of equilibrium either by the coupling to several heat baths of different temperature or by time-periodic driving in combination with the coupling to a heat bath. Within the framework of (Floquet-)Born-Markov theory, several analytical and numerical methods are described in detail. This includes a mean-field theory in terms of occupation numbers, an augmented mean-field theory taking into account also nontrivial two-particle correlations, and quantum-jump-type Monte Carlo simulations. For the case of the ideal Fermi gas, these methods are applied to simple lattice models and the possibility of achieving exotic states via bath engineering is pointed out. The largest part of this work is devoted to bosonic quantum gases and the phenomenon of Bose selection, a nonequilibrium generalization of Bose condensation, where multiple single-particle states are selected to acquire a large occupation [Phys. Rev. Lett. 111, 240405 (2013)]. In this context, among others, we provide a theory for transitions where the set of selected states changes, describe an efficient algorithm for finding the set of selected states, investigate beyond-mean-field effects, and identify the dominant mechanisms for heat transport in the Bose-selected state.
The study of out-of-equilibrium dynamics in ultra-cold gases is a new and exciting field, driven largely by the recent experimental advances in controlling and imaging cold clouds. The experimental and theoretical work thus far has been somewhat exploratory and largely numerical in nature, as the very paradigms for thinking about these systems are not well established. In this thesis I consider several different scenarios of ultra-cold bosonic and fermionic gases driven out of equilibrium and study their properties. In Chapter 1, I provide an overview of the phenomenology of ultra-cold gases, highlighting the timescales governing these systems and how the experimentalist can tune them. I discuss how cold gases can be cooled and trapped and discuss the basic physics behind optical lattices. I also discuss experimental probes of these gases, in particular the new high resolution imaging techniques developed recently at Chicago, Munich and Harvard. In Chapter 2, I discuss an early experiment (circa. 2008) which observed long lived spin dynamics in a thermal spin-1/2 Fermi gas. This experiment is an nice illustration of interesting physics resulting from the separation of timescales between spin and collisional dynamics. In my opinion, it is an excellent example of why cold gases are naturally suited to studying non-equilibrium dynamics. I simulate the experiment numerically using a collisionless Boltzmann equation and explain the observed spin dynamics both qualitatively and quantitively. In Chapter 3, I continue the discussion of spin waves in thermal gases by extending previous works on spin-1/2 gases to spin-1 Bose gases. In contrast to Chapter 2, the bulk of the work in this Chapter is analytic in nature. In particular, I find a spin wave instability in the thermal spin-1 Bose gas, which is the high temperature analog of the polar to ferromagnetic transition in a spin-1 Bose Einstein condensate. In Chapter 3, I turn my attention to bosonic systems and briefly review the the Bogoliubov mean-field theory. I calculate the momentum distribution and density-density correlation function of an interacting Bose gas within the Bogoliubov framework. Then I consider bosons in an optical lattice, and introduce the Bose Hubbard model. I calculate the mean-field phase diagram of the Bose Hubbard model and then consider fluctuations about the mean field, and derive the excitation spectrum of the lattice gas in the superfluid and insulating regimes. In Chapter 4, I ask what we learn by studying the dynamics of correlation functions following a sudden change in the interactions in a superfluid. Using the Bogoliubov theory developed in Chapter 3, I will show how the underlying excitation spectrum influences the long and short time behavior of the correlation functions. By considering a lattice dispersion, I study the analogous problem in a weak optical lattice and discuss how the lattice dispersion leads to additional features in the correlation functions. I will also discuss the timescale governing the revival of the condensate fraction in a quantum depleted gas. In Chapter 5, I derive equations of motion governing the dynamics of one and two body correlation functions in the single-band Bose Hubbard model, applicable to bosons in deep lattices. I then consider a simple quench from a Mott insulating initial state to a weakly interacting final state and produce analytic expressions describing the dynamics of correlations following such a quench. I discuss the timescale for the development of long range order following such a quench. I study the problem of chapter 4 using an equations of motion approach. This approach complements the Bogoliubov approach of Chapter 4. First, I derive exact expressions for a quench to a non-interacting state. I then consider how interactions redistribute quasi-momentum to first order in perturbation theory in different dimensions. In Chapter 6, I calculate the relevant timescales for local and global dynamics in trapped lattice Bose gases, a work done in collaboration with Dr. Kaden R. A Hazzard. Using a time-dependent Gutzwiller mean-field theory, I show that the timescale for local equilibration in these systems is fast in experimental terms. I then show that due to the spatial inhomogeneities inherent to cold gases, achieving global equilibrium can be quite complicated, sometimes taking longer than the lifetime of the experiment, an issue of practical importance to current day experiments. I continue this discussion in Chapter 7 which is a collaborative work with experimentalists David McKay and Prof. Brian DeMarco from the University of Toronto and the University of Illinois, Urbana Champaign. Using experimental and numerical methods, we show that the rapid timescales for local dynamics in interacting systems invalidates a frequently used cold atom technique for mapping out the momentum distribution of atoms in an optical lattice.
Abstract We present a theoretical review of the recent progress in non-equilibrium BCS (Bardeen-Cooper-Schrieffer)-BEC (Bose-Einstein condensation) crossover physics. As a paradigmatic example, we consider a strongly interacting driven-dissipative two-component Fermi gas where the non-equilibrium steady state is tuned by adjusting the chemical potential difference between two reservoirs that are coupled with the system. As a powerful theoretical tool to deal with this system, we employ the Schwinger-Keldysh Green’s function technique. We systematically evaluate the superfluid transition, as well as the single-particle properties, in the non-equilibrium BCS-BEC crossover region, by adjusting the chemical potential difference between the reservoirs and the strength of an s-wave pairing interaction associated with a Feshbach resonance. In the weak-coupling BCS side, the chemical potential difference is shown to imprint a two-step structure on the particle momentum distribution, leading to an anomalous enhancement of pseudogap, as well as the emergence of exotic Fulde-Ferrell-Larkin-Ovchinnikov-type superfluid instability. Since various non-equilibrium situations have recently been realized in ultracold Fermi gases, the theoretical understanding of non-equilibrium BCS-BEC crossover physics would become increasingly important in this research field.
We report on the experimental observation of stimulated cooling in the non-equilibrium Bose-Einstein condensate (BEC) of weakly interacting exciton-polaritons from approximately room temperature down to 20K. By resolving the condensate in energy-momentum space and performing interferometric measurements, we distinguish the condensate from thermalized particles yet occupying excited states macroscopically. In contrast to the analytical quantum theories of non-equilibrium BEC [Shishkov et al., Phys. Rev. Lett. 128, 065301 (2022)], we observe segmentation of the particle density along the excited states into two fractions both following Bose-Einstein distribution, albeit with different effective temperatures and chemical potentials. Our results indicate that the temperature of the weakly interacting Bose gas is universally set by the density-dependent chemical potential, revealing a defining property of non-equilibrium BECs. Finally, we demonstrate that the stimulated nature of the cooling process directly governs the emergence of quantum coherence of the condensate and shapes the dissipative properties of the excited states.