Driven-dissipative physics lie at the core of quantum optics. However, the full interplay between a driven quantum many-body system and its environment remains relatively unexplored in the solid state realm. In this Letter, we inspect this interplay beyond the commonly employed stroboscopic Hamiltonian picture based on the specific example of a driven superconductor. Using the Shirley-Floquet and Keldysh formalisms as well as a generalization of the notion of superconducting fitness to the driven case, we show how a drive which anticommutes with the superconducting gap operator generically induces an unusual particle-hole structure in the spectral functions from the perspective of the thermal bath. Concomitant with a driving frequency which is near resonant with the intrinsic cutoff frequency of the underlying interaction, this spectral structure can be harnessed to enhance the superconducting transition temperature. Our work paves the way for further studies for driven-dissipative engineering of exotic phases of matter in solid-state systems.
Driven-dissipative physics lie at the core of quantum optics. However, the full interplay between a driven quantum many-body system and its environment remains relatively unexplored in the solid state realm. In this Letter, we inspect this interplay beyond the commonly employed stroboscopic Hamiltonian picture based on the specific example of a driven superconductor. Using the Shirley-Floquet and Keldysh formalisms as well as a generalization of the notion of superconducting fitness to the driven case, we show how a drive which anticommutes with the superconducting gap operator generically induces an unusual particle-hole structure in the spectral functions from the perspective of the thermal bath. Concomitant with a driving frequency which is near resonant with the intrinsic cutoff frequency of the underlying interaction, this spectral structure can be harnessed to enhance the superconducting transition temperature. Our work paves the way for further studies for driven-dissipative engineering of exotic phases of matter in solid-state systems.
Intense time-periodic laser fields can transform the electronic structure of a solid into strongly modified Floquet-Bloch bands. While this suggests multiple pathways to induce electronic orders such as superconductivity or charge density waves, the possibility of preparing low-energy phases of Floquet Hamiltonians remains unclear because of the energy absorption at typical experimentally accessible driving frequencies. Here we investigate a realistic pathway towards laser control of electronic orders, which is the transient enhancement of fluctuating orders. Using a conserving Keldysh Green's function formalism, we simulate the buildup of short range Cooper-pair correlations out of a normal metal in the driven attractive Hubbard model. Even for frequencies only slightly above or within the bandwidth, a substantial enhancement of correlations can be achieved before the system reaches a high electronic temperature. This behavior relies on the nonthermal nature of the driven state. The effective temperature of the electrons at the Fermi surface, which more closely determines the superconducting correlations, remains lower than an estimate from the global energy density. Even though short ranged, the fluctuations can have marked signatures in the electronic spectra.
Floquet engineering, the control of a quantum system by means of time-periodic driving, allows to modify the properties of a system so that it is described by an approximate effective time-independent Hamiltonian. However, in the presence of interactions the stabilization of interesting many-body ground states of such effective Hamiltonians is possible only on a certain time scale, beyond which Floquet heating sets in, as it results from unwanted driving induced resonant excitation. Moreover, the preparation of the ground state of such Floquet engineered effective Hamiltonians usually has to be accomplished adiabatically, which is another source of heating, especially when a phase transition has to be passed in a large system. Here, we propose a general dissipative strategy for the preparation and stabilization of effective ground states that are protected by an energy gap, such as topologically ordered states. It is scalable and relies on coupling the driven system to a thermal bath, the properties of which are chosen so that it both suppresses Floquet heating and guides the system into a non-equilibrium steady state with a large occupation of the effective ground-state. The small residual occupations of effective excited states are non-thermal, reflecting the non-equilibrium nature of the scheme. We use the Floquet-Born-Markov master equation to verify the proposed strategy. In particular, we discuss the preparation of both a one-dimensional Mott insulator and a two-dimensional fractional Chern insulator in strongly driven Bose-Hubbard systems.
Understanding quantum coherence and proposing protection mechanisms has become one of the fundamental challenges in quantum physics research. We investigate a generic driven open quantum system, i.e., the driven spin-boson model, beyond the rotating-wave approximation. Although steady-state coherence vanishes in Floquet-Markov and Bloch-Redfield approaches, it becomes finite within a time-non-local master equation with a memory kernel. We analytically reveal that the steady-state coherence is associated with the overlap between the spectral densities associated with neighboring Floquet quasifrequencies. Motivated by this, we show that increasing temperature and introducing mixed transverse and longitudinal baths broadens the spectral density, thereby enhancing steady-state coherence. This is described by resonance fluorescence spectra, which exhibit clear spectral broadening and enhanced steady-state values. For a transverse dissipative coupling to the bath, three transition frequencies emerge in the Floquet basis, corresponding to the Mollow triplet. For weak resonant driving, these quasienergies become nearly degenerate, leading to closely spaced peaks in the resonance fluorescence spectrum, and the steady-state quantum coherence asymptotically approaches its maximum. For a longitudinal coupling to the bath, the quantum system exhibits a single transition frequency, thereby resulting in a complete suppression of the steady-state quantum coherence. We systematically investigate the influences of driving strength, frequency, temperature, and various dissipative baths on steady-state quantum coherence. These findings provide a foundational framework for efficiently engineering steady-state quantum coherence in nanoscale open quantum devices under optical field excitation.
Driven-dissipative qubit-resonator dynamics, which are the basis of most dispersive superconducting qubit measurement schemes, are often modeled with Lindblad master equations built from subsystem local jump operators, even when the qubit and resonator are appreciably hybridized. In this work we revisit this setting using a microscopic Bloch-Redfield approach, where dissipation is constructed in the eigenbasis of the coupled qubit-resonator Hamiltonian with a complete, frequency dependent, open system description of the transmission line environment. Here, we show that the Lindblad and Bloch-Redfield decay rates can be quantitatively different in the absence of driving, while in the driven case we demonstrate that the time-independent Redfield dissipator and its time-dependent generalization can show qualitatively different behaviors as a function of driving strength. Finally, we investigate the effects of driving in structured spectral densities, recovering the suppression of measurement-induced relaxation in the presence of a so called Purcell filter.
Periodically-driven (Floquet) quantum systems are ubiquitous in science and technology. For example, when a laser illuminates a material or an AC voltage is applied to a device, the system is well-described by a time-periodic Hamiltonian. In recent years, periodic driving has been proposed, not just as a tool to excite and probe devices, but actually as a mechanism of engineering new phases of matter, some of which have no equilibrium analog. However, with this promise comes a serious problem. Intuitively, if energy is injected into and distributed throughout a system, it is no surprise that it tends to heat up indefinitely to infinite temperature. In this thesis, we study the mechanisms of heating, i.e. the process of thermalization, in Floquet systems and propose methods to control them. Specifically, for non-interacting Floquet systems that are coupled to external bosonic and fermionic baths (e.g. laser-driven electrons in a semiconductor that interact with phonons and an external lead), we classify the relevant scattering processes that contribute to cooling/heating in the Floquet bands and suggest methods to suppress heating via bandwidth-restrictions on the baths. We find that is possible, with appropriate dissipative engineering, to stabilize a controlled incompressible nonequilibrium steady-state resembling a ground state - a state we term the "Floquet insulator." We extend this analysis to include short-range interactions that contribute additional heating processes and show, under the same framework, that heating can be controlled with dissipation. In the process, we develop a simple effective model for the Floquet band densities that captures the essence of all the Floquet scattering processes and that is useful for ballparking experimentally-relevant estimates of heating. Next, we turn our attention to strongly-interacting closed Floquet systems and study how heating emerges through a proliferation of resonances. We find a novel integrable point governing the strong-interaction limit of the Floquet system and examine the breakdown of integrability via the proliferation of resonances. We observe two distinct scaling regimes, attributed to non-thermal and thermal behavior, and discover a power-law scaling of the crossover between them as a function of system size. The lingering ergodicity-breaking effects of the conserved quantities in the vicinity (in parameter space) of the integrable point at finite size is a phenomena we term "near-integrability." These results suggest that small quantum systems, which are accessible currently in many platforms (e.g. trapped ions, cold atoms, superconducting devices), intrinsically host non-thermal states that one may be able to utilize to avoid heating. Furthermore, our results suggest a "dual" interpretation, in the thermodynamic limit, that a periodically-driven system exhibits prethermalization as a power-law in interaction strength.
In circuit quantum electrodynamical systems, the quasiparticle-related losses in Josephson junctions are suppressed due to the gap in the superconducting density of states which is much higher than the typical energy of a microwave photon. In this work, we show that a strong drive even at a frequency lower than twice the superconductor gap parameter can activate dissipation in the junctions due to photon-assisted breaking of the Cooper pairs. Both the decay rate and noise strength associated with the losses are sensitive to the dc phase bias of the junction and can be tuned in a broad range by the amplitude and the frequency of the external driving field, making the suggested mechanism potentially attractive for designing tunable dissipative elements. We also predict pronounced memory effects in the driven Josephson junctions, which are appealing for both theoretical and experimental studies of non-Markovian physics in superconducting quantum circuits. We illustrate our theoretical findings by studying the spectral properties and the steady-state population of a low-impedance resonator coupled to the driven Josephson junction: we show the emergence of non-Lorentzian spectral lines and broad tunability of effective temperature of the steady state.