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arXiv2012

Quantum dynamics and entanglement of a 1D Fermi gas released from a trap

We investigate the entanglement properties of the nonequilibrium dynamics of one-dimensional noninteracting Fermi gases released from a trap. The gas of N particles is initially in the ground state within hard-wall or harmonic traps, then it expands after dropping the trap. We compute the time dependence of the von Neumann and Renyi entanglement entropies and the particle fluctuations of spatial intervals around the original trap, in the limit of a large number N of particles. The results for these observables apply to one-dimensional gases of impenetrable bosons as well. We identify different dynamical regimes at small and large times, depending also on the initial condition, whether it is that of a hard-wall or harmonic trap. In particular, we analytically show that the expansion from hard-wall traps is characterized by the asymptotic small-time behavior $S \approx (1/3)\ln(1/t)$ of the von Neumann entanglement entropy, and the relation $S\approx π^2 V/3$ where V is the particle variance, which are analogous to the equilibrium behaviors whose leading logarithms are essentially determined by the corresponding conformal field theory with central charge $c=1$. The time dependence of the entanglement entropy of extended regions during the expansion from harmonic traps shows the remarkable property that it can be expressed as a global time-dependent rescaling of the space dependence of the initial equilibrium entanglement entropy.

cond-mat.stat-mech↗

arXiv2013

Dependence of a quantum mechanical system on its own initial state and the initial state of the environment it interacts with

We present a unifying framework to the understanding of when and how quantum mechanical systems become independent of their initial conditions and adapt macroscopic properties (like temperature) of the environment.By viewing this problem from an quantum information theory perspective, we are able to simplify it in a very natural and easy way. We first show that for any interaction between the system and the environment, and almost all initial states of the system, the question of how long the system retains memory of its initial conditions can be answered by studying the temporal evolution of just one special initial state. This special state thereby depends only on our knowledge of macroscopic parameters of the system. We provide a simple entropic inequality for this state that can be used to determine whether mosts states of the system have, or have not become independent of their initial conditions after time $t$. We discuss applications of our entropic criterion to thermalization times in systems with an effective light-cone and to quantum memories suffering depolarizing noise. We make a similar statement for almost all initial states of the environment, and finally provide a sufficient condition for which a system never thermalizes, but remains close to its initial state for all times.

quant-ph↗

arXiv2013

Approximating random quantum optimization problems

We report a cluster of results regarding the difficulty of finding approximate ground states to typical instances of the quantum satisfiability problem $k$-QSAT on large random graphs. As an approximation strategy, we optimize the solution space over `classical' product states, which in turn introduces a novel autonomous classical optimization problem, PSAT, over a space of continuous degrees of freedom rather than discrete bits. Our central results are: (i) The derivation of a set of bounds and approximations in various limits of the problem, several of which we believe may be amenable to a rigorous treatment. (ii) A demonstration that an approximation based on a greedy algorithm borrowed from the study of frustrated magnetism performs well over a wide range in parameter space, and its performance reflects structure of the solution space of random $k$-QSAT. Simulated annealing exhibits metastability in similar `hard' regions of parameter space. (iii) A generalization of belief propagation algorithms introduced for classical problems to the case of continuous spins. This yields both approximate solutions, as well as insights into the free energy `landscape' of the approximation problem, including a so-called dynamical transition near the satisfiability threshold. Taken together, these results allow us to elucidate the phase diagram of random $k$-QSAT in a two-dimensional energy-density--clause-density space.

cond-mat.stat-mech↗

arXiv2013

Comparative investigation of the freezing phenomena for quantum correlations under nondissipative decoherence

We show that the phenomenon of frozen discord, exhibited by specific classes of two-qubit states under local nondissipative decoherent evolutions, is a common feature of all known bona fide measures of general quantum correlations. All those measures, despite inducing typically inequivalent orderings on the set of nonclassically correlated states, return a constant value in the considered settings. Every communication protocol which relies on quantum correlations as resource will run with a performance completely unaffected by noise in the specified dynamical conditions. We provide a geometric interpretation of this

quant-ph↗

arXiv2013

Unidirectional quantum walks: evolution and exit times

In this paper we focus our attention on a particle that follows a unidirectional quantum walk, an alternative version of the nowadays widespread discrete-time quantum walk on a line. Here the walker at each time step can either remain in place or move in a fixed direction, e.g., rightward or upward. While both formulations are essentially equivalent, the present approach leads to consider Discrete Fourier Transforms, which eventually results in obtaining explicit expressions for the wave functions in terms of finite sums, and allows the use of efficient algorithms based on the Fast Fourier Transform. The wave functions here obtained govern the probability of finding the particle at any given location, but determine as well the exit-time probability of the walker from a fixed interval, which is also analyzed.

quant-ph↗

arXiv2013

Thermalized polarization dynamics of a discrete optical waveguide system with four-wave mixing

Statistical mechanics of two coupled vector fields is studied in the tight-binding model that describes propagation of polarized light in discrete waveguides in the presence of the four-wave mixing. The energy and power conservation laws enable the formulation of the equilibrium properties of the polarization state in terms of the Gibbs measure with positive temperature. The transition line $T=\infty$ is established beyond which the discrete vector solitons are created. Also in the limit of the large nonlinearity an analytical expression for the distribution of Stokes parameters is obtained which is found to be dependent only on the statistical properties of the initial polarization state and not on the strength of nonlinearity. The evolution of the system to the final equilibrium state is shown to pass through the intermediate stage when the energy exchange between the waveveguides is still negligible. The distribution of the Stokes parameters in this regime has a complex multimodal structure strongly dependent on the nonlinear coupling coefficients and the initial conditions.

cond-mat.stat-mech↗

arXiv2013

Action principle for continuous quantum measurement

We present a stochastic path integral formalism for continuous quantum measurement that enables the analysis of rare events using action methods. By doubling the quantum state space to a canonical phase space, we can write the joint probability density function of measurement outcomes and quantum state trajectories as a phase space path integral. Extremizing this action produces the most-likely paths with boundary conditions defined by preselected and postselected states as solutions to a set of ordinary differential equations. As an application, we analyze continuous qubit measurement in detail and examine the structure of a quantum jump in the Zeno measurement regime.

quant-ph↗

arXiv2013

Entropy production and information fluctuations along quantum trajectories

Employing the stochastic wave function method, we study quantum features of stochastic entropy production in nonequilibrium processes of open systems. It is demonstarted that continuous measurements on the environment introduce an additional, non-thermal contribution to the entropy flux, which is shown to be a direct consequence of quantum fluctuations. These features lead to a quantum definition of single trajectory entropy contributions, which accounts for the difference between classical and quantum trajectories and results in a quantum correction to the standard form of the integral fluctuation theorem.

quant-ph↗

arXiv2013

Gaussian entanglement induced by an extended thermal environment

We study stationary entanglement among three harmonic oscillators which are dipole coupled to a one-dimensional or a three-dimensional bosonic environment. The analysis of the open-system dynamics is performed with generalized quantum Langevin equations which we solve exactly in Fourier representation. The focus lies on Gaussian bipartite and tripartite entanglement induced by the highly non-Markovian interaction mediated by the environment. This environment-induced interaction represents an effective many-parties interaction with a spatial long-range feature: a main finding is that the presence of a passive oscillator is detrimental for the stationary two-mode entanglement. Furthermore, our results strongly indicate that the environment-induced entanglement mechanism corresponds to uncontrolled feedback which is predominantly coherent at low temperatures and for moderate oscillator-environment coupling as compared to the oscillator frequency.

quant-ph↗

arXiv2013

Thermodynamic Work Gain from Entanglement

We show that entanglement can be utilized to extract thermodynamic work beyond classical correlation via feedback control based on measurement on part of a composite system. The net work gain due to entanglement is determined by the change in the mutual information content between the subsystems that is accessible by the memory.

quant-ph↗

arXiv2013

Soft quantum vibrations of PT-symmetric nonlinear ion chain

We theoretically study the quantum dynamics of transverse vibrations of a one-dimensional chain of trapped ions in harmonic potentials interacting via a Reggeon-type cubic nonlinearity that is nonunitary but preserves PT symmetry. We propose the notion of quantum fragility for the dissipative structural phase transition that spontaneously breaks the PT symmetry. In the quantum fragile regime, the nonlinearity dominates the response to mechanical perturbations and the chain supports neither the ordinary quantum phonons of a Luttinger liquid, nor the supersonic solitons that arise in classical fragile critical points in the absence of fluctuations. Quantum fluctuations, approximately captured within a one-loop renormalization group, give rise to mechanical excitations with a strongly momentum-dependent phonon velocity and dissipative spectral behavior. Observable signatures of the quantum fragile chain in trapped ion systems are discussed.

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arXiv2013

Topological phase transitions driven by non-Abelian gauge potentials in optical square lattices

We analyze a tight-binding model of ultracold fermions loaded in an optical square lattice and subjected to a synthetic non-Abelian gauge potential featuring both a magnetic field and a translationally invariant SU(2) term. We consider in particular the effect of broken time-reversal symmetry and its role in driving non-trivial topological phase transitions. By varying the spin-orbit coupling parameters, we find both a semimetal/insulator phase transition and a topological phase transition between insulating phases with different numbers of edge states. The spin is not a conserved quantity of the system and the topological phase transitions can be detected by analyzing its polarization in time of flight images, providing a clear diagnostic for the characterization of the topological phases through the partial entanglement between spin and lattice degrees of freedom.

cond-mat.quant-gas↗

arXiv2013

Criticality, factorization and long-range correlations in the anisotropic XY-model

We study the long-range quantum correlations in the anisotropic XY-model. By first examining the thermodynamic limit we show that employing the quantum discord as a figure of merit allows one to capture the main features of the model at zero temperature. Further, by considering suitably large site separations we find that these correlations obey a simple scaling behavior for finite temperatures, allowing for efficient estimation of the critical point. We also address ground-state factorization of this model by explicitly considering finite size systems, showing its relation to the energy spectrum and explaining the persistence of the phenomenon at finite temperatures. Finally, we compute the fidelity between finite and infinite systems in order to show that remarkably small system sizes can closely approximate the thermodynamic limit.

quant-ph↗

arXiv2013

Quantum computational universality of spin-3/2 Affleck-Kennedy-Lieb-Tasaki states beyond the honeycomb lattice

Universal quantum computation can be achieved by simply performing single-spin measurements on a highly entangled resource state, such as cluster states. The family of Affleck-Kennedy-Lieb-Tasaki (AKLT) states has recently been explored; for example, the spin-1 AKLT chain can be used to simulate single-qubit gate operations on a single qubit, and the spin-3/2 two-dimensional AKLT state on the honeycomb lattice can be used as a universal resource. However, it is unclear whether such universality is a coincidence for the specific state or a shared feature in all two-dimensional AKLT states. Here we consider the family of spin-3/2 AKLT states on various trivalent Archimedean lattices and show that in addition to the honeycomb lattice, the spin-3/2 AKLT states on the square octagon $(4,8^2)$ and the `cross' $(4,6,12)$ lattices are also universal resource, whereas the AKLT state on the `star' $(3,12^2)$ lattice is likely not due to geometric frustration.

quant-ph↗

arXiv2013

Universal scaling at non-thermal fixed points of a two-component Bose gas

Quasi-stationary far-from-equilibrium critical states of a two-component Bose gas are studied in two spatial dimensions. After the system has undergone an initial dynamical instability it approaches a non-thermal fixed point. At this critical point the structure of the gas is characterised by ensembles of (quasi-)topological defects such as vortices, skyrmions and solitons which give rise to universal power-law behaviour of momentum correlation functions. The resulting power-law spectra can be interpreted in terms of strong-wave-turbulence cascades driven by particle transport into long-wave-length excitations. Scaling exponents are determined on both sides of the miscible-immiscible transition controlled by the ratio of the intra-species to inter-species couplings. Making use of quantum turbulence methods, we explain the specific values of the exponents from the presence of transient (quasi-)topological defects.

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arXiv2017

Detecting metrologically useful asymmetry and entanglement by a few local measurements

Important properties of a quantum system are not directly measurable, but they can be disclosed by how fast the system changes under controlled perturbations. In particular, asymmetry and entanglement can be verified by reconstructing the state of a quantum system. Yet, this usually requires experimental and computational resources which increase exponentially with the system size. Here we show how to detect metrologically useful asymmetry and entanglement by a limited number of measurements. This is achieved by studying how they affect the speed of evolution of a system under a unitary transformation. We show that the speed of multiqubit systems can be evaluated by measuring a set of local observables, providing exponential advantage with respect to state tomography. Indeed, the presented method requires neither the knowledge of the state and the parameter-encoding Hamiltonian nor global measurements performed on all the constituent subsystems. We implement the detection scheme in an all-optical experiment.

quant-ph↗

arXiv2018

A unified theory for excited-state, fragmented, and equilibrium-like Bose condensation in pumped photonic many-body systems

We derive a theory for Bose condensation in nonequilibrium steady states of bosonic quantum gases that are coupled both to a thermal heat bath and to a pumped reservoir (or gain medium), while suffering from loss. Such a scenario describes photonic many-body systems such as exciton-polariton gases. Our analysis is based on a set of kinetic equations for a gas of noninteracting bosons. By identifying a dimensionless scaling parameter controlling the boson density, we derive a sharp criterion for which system states become selected to host a macroscopic occupation. We show that with increasing pump power, the system generically undergoes a sequence of nonequilibrum phase transitions. At each transition a state either becomes or ceases to be Bose selected (i.e. to host a condensate): The state which first acquires a condensate when the pumping exceeds a threshold is the one with the largest ratio of pumping to loss. This intuitive behavior resembles simple lasing. In the limit of strong pumping, the coupling to the heat bath becomes dominant so that eventually the ground state is selected, corresponding to equilibrium(-like) Bose condensation. For intermediate pumping strengths, several states become selected giving rise to fragmented nonequilibrium Bose condensation. We compare these predictions to experimental results obtained for excitons polaritons in a double-pillar structure [Phys. Rev. Lett. 108, 126403 (2012)] and find good agreement. Our theory, moreover, predicts that the reservoir occupation is clamped at a constant value whenever the system hosts an odd number of Bose condensates.

cond-mat.stat-mech↗

arXiv2022

Absence and recovery of cost-precision tradeoff relations in quantum transport

The operation of many classical and quantum systems in nonequilibrium steady state is constrained by cost-precision (dissipation-fluctuation) tradeoff relations, delineated by the thermodynamic uncertainty relation (TUR). However, coherent quantum electronic nanojunctions can escape such a constraint, showing finite charge current and nonzero entropic cost with vanishing current fluctuations. Here, we analyze the absence, and restoration, of cost-precision tradeoff relations in fermionic nanojunctions under different affinities: voltage and temperature biases. With analytic work and simulations, we show that both charge and energy currents can display the absence of cost-precision tradeoff if we engineer the transmission probability as a boxcar function -- with a perfect transmission and hard energy cutoffs. Specifically for charge current under voltage bias, the standard TUR may be immediately violated as we depart from equilibrium, and it is exponentially suppressed with increased voltage. However, beyond idealized, hard-cutoff energy-filtered transmission functions, we show that realistic models with soft cutoffs or imperfect transmission functions follow cost-precision tradeoffs, and eventually recover the standard TUR sufficiently far from equilibrium. The existence of cost-precision tradeoff relations is thus suggested as a generic feature of realistic nonequilibrium quantum transport junctions.

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