We add quantum fluctuations to a classical Hamiltonian model with synchronized period doubling in the thermodynamic limit, replacing the $N$ classical interacting angular momenta with quantum spins of size $l$. The full permutation symmetry of the Ha
miltonian allows a mapping to a bosonic model and the application of exact diagonalization for quite large system size. {In the thermodynamic limit $Ntoinfty$ the model is described by a system of Gross-Pitaevski equations whose classical-chaos properties closely mirror the finite-$N$ quantum chaos.} For $Ntoinfty$, and $l$ finite, Rabi oscillations mark the absence of persistent period doubling, which is recovered for $ltoinfty$ with Rabi-oscillation frequency tending exponentially to 0. For the chosen initial conditions, we can represent this model in terms of Pauli matrices and apply the discrete truncated Wigner approximation. For finite $l$ this approximation reproduces no Rabi oscillations but correctly predicts the absence of period doubling. Quantitative agreement is recovered in the classical $ltoinfty$ limit.
Recent predictions for quantum-mechanical enhancements in the operation of small heat engines have raised renewed interest in their study from both a fundamental perspective and in view of applications. One essential question is whether collective ef
fects may help to carry enhancements over larger scales, when increasing the number of systems composing the working substance of the engine. Such enhancements may consider not only power and efficiency, that is its performance, but, additionally, its constancy, i.e. the stability of the engine with respect to unavoidable environmental fluctuations. We explore this issue by introducing a many-body quantum heat engine model composed by spin pairs working in continuous operation. We study how power, efficiency and constancy scale with the number of spins composing the engine, and obtain analytical expressions in the macroscopic limit. Our results predict power enhancements, both in finite-size and macroscopic cases, for a broad range of system parameters and temperatures, without compromising the engine efficiency, as well as coherence-enhanced constancy for large but finite sizes. We also discuss these quantities in connection to Thermodynamic Uncertainty Relations (TUR).
We investigate measurement-induced phase transitions in the Quantum Ising chain coupled to a monitoring environment. We compare two different limits of the measurement problem, the stochastic quantum-state diffusion protocol corresponding to infinite
small jumps per unit of time and the no-click limit, corresponding to post-selection and described by a non-Hermitian Hamiltonian. In both cases we find a remarkably similar phenomenology as the measurement strength $gamma$ is increased, namely a sharp transition from a critical phase with logarithmic scaling of the entanglement to an area-law phase, which occurs at the same value of the measurement rate in the two protocols. An effective central charge, extracted from the logarithmic scaling of the entanglement, vanishes continuously at the common transition point, although with different critical behavior possibly suggesting different universality classes for the two protocols. We interpret the central charge mismatch near the transition in terms of noise-induced disentanglement, as suggested by the entanglement statistics which displays emergent bimodality upon approaching the critical point. The non-Hermitian Hamiltonian and its associated subradiance spectral transition provide a natural framework to understand both the extended critical phase, emerging here for a model which lacks any continuous symmetry, and the entanglement transition into the area law.
We consider a finite quantum system under slow driving and weakly coupled to thermal reservoirs at different temperatures. We present a systematic derivation of the quantum master equation for the density matrix and the out-of-time-order correlators.
We start from the microscopic Hamiltonian and we formulate the equations ruling the dynamics of these quantities by recourse to the Schwinger-Keldysh non-equilibrium Greens function formalism, performing a perturbative expansion in the coupling between the system and the reservoirs. We focus on the adiabatic dynamics, which corresponds to considering the linear response in the ratio between the relaxation time due to the system-reservoir coupling and the time scale associated to the driving. We calculate the particle and energy fluxes. We illustrate the formalism in the case of a qutrit coupled to bosonic reservoirs and of a pair of interacting quantum dots attached to fermionic reservoirs, also discussing the relevance of coherent effects.
The characterization and control of quantum effects in the performance of thermodynamic tasks may open new avenues for small thermal machines working in the nanoscale. We study the impact of coherence in the energy basis in the operation of a small t
hermal machine which can act either as a heat engine or as a refrigerator. We show that input coherence may enhance the machine performance and allow it to operate in otherwise forbidden regimes. Moreover, our results also indicate that, in some cases, coherence may also be detrimental, rendering optimization of particular models a crucial task for benefiting from coherence-induced enhancements.
Controlling the spread of correlations in quantum many-body systems is a key challenge at the heart of quantum science and technology. Correlations are usually destroyed by dissipation arising from coupling between a system and its environment. Here,
we show that dissipation can instead be used to engineer a wide variety of spatio-temporal correlation profiles in an easily tunable manner. We describe how dissipation with any translationally-invariant spatial profile can be realized in cold atoms trapped in an optical cavity. A uniform external field and the choice of spatial profile can be used to design when and how dissipation creates or destroys correlations. We demonstrate this control by preferentially generating entanglement at a desired wavevector. We thus establish non-local dissipation as a new route towards engineering the far-from-equilibrium dynamics of quantum information, with potential applications in quantum metrology, state preparation, and transport.
We investigate superradiant-like dynamics of the nuclear-spin bath in a single-electron quantum dot, by considering electrons cyclically shuttling on/off an isotopically enriched `nuclear-spin island. Assuming a uniform hyperfine interaction, we disc
uss in detail the nuclear spin evolution under shuttling and its relation to superradiance. We derive the minimum shuttling time which allows to escape the adiabatic spin evolution. Furthermore, we discuss slow/fast shuttling under the inhomogeneous field of a nearby micromagnet. Finally, by comparing our scheme to a model with stationary quantum dot, we stress the important role played by non-adiabatic shuttling in lifting the Coulomb blockade and thus establishing the superradiant-like behavior.
Finding the exact counterdiabatic potential is, in principle, particularly demanding. Following recent progresses about variational strategies to approximate the counterdiabatic operator, in this paper we apply this technique to the quantum annealing
of the $p$-spin model. In particular, for $ p = 3 $ we find a new form of the counterdiabatic potential originating from a cyclic ansatz, that allows us to have optimal fidelity even for extremely short dynamics, independently of the size of the system. We compare our results with a nested commutator ansatz, recently proposed in P. W. Claeys, M. Pandey, D. Sels, and A. Polkovnikov, Phys. Rev. Lett. 123, 090602 (2019), for $ p = 1 $ and $ p = 3 $. We also analyze generalized $ p $-spin models to get a further insight into our ansatz.
We explore the possibility of enhancing the performance of small thermal machines by the presence of common noise sources. In particular, we study a prototypical model for an autonomous quantum refrigerator comprised by three qubits coupled to therma
l reservoirs at different temperatures. Our results show that engineering the coupling to the reservoirs to act as common environments lead to relevant improvements in the performance. The enhancements arrive to almost double the cooling power of the original fridge without compromising its efficiency. The greater enhancements are obtained when the refrigerator may benefit from the presence of a decoherence-free subspace. The influence of coherent effects in the dissipation due to one- and two-spin correlated processes is also examined by comparison with an equivalent incoherent yet correlated model of dissipation.
We provide evidence that a clean kicked Bose-Hubbard model exhibits a many-body dynamically localized phase. This phase shows ergodicity breaking up to the largest sizes we were able to consider. We argue that this property persists in the limit of l
arge size. The Floquet states violate eigenstate thermalization and then the asymptotic value of local observables depends on the initial state and is not thermal. This implies that the system does not generically heat up to infinite temperature, for almost all the initial states. Differently from many-body localization here the entanglement entropy linearly increases in time. This increase corresponds to space-delocalized Floquet states which are nevertheless localized across specific subsectors of the Hilbert space: In this way the system is prevented from randomly exploring all the Hilbert space and does not thermalize.
