Dissipative Phase Transition Research Articles

Interaction-induced dissipative quantum phase transition in a head-to-tail atomic Josephson junction

Interaction-induced dissipative quantum phase transition in a head-to-tail atomic Josephson junction

Controlling Matter Phases beyond Markov.

Controlling phase transitions in quantum systems via coupling to reservoirs has been mostly studied for idealized memory-less environments under the so-called Markov approximation. Yet, most quantum materials and experiments in the solid state, atomic, molecular and optical physics are coupled to reservoirs with finite memory times. Here, using the spectral theory of non-Markovian dissipative phase transitions developed in the companion paper [Debecker, Martin, and Damanet (to be published)], we show that memory effects can be leveraged to reshape matter phase boundaries, but also reveal the existence of dissipative phase transitions genuinely triggered by non-Markovian effects.

Spectral theory of non-Markovian dissipative phase transitions

Spectral theory of non-Markovian dissipative phase transitions

Nonequilibrium Transition between Dissipative Time Crystals

We show a dissipative phase transition in a driven nonlinear quantum oscillator in which a discrete time-translation symmetry is spontaneously broken in two different ways. The corresponding regimes display either discrete or incommensurate time-crystal order, which we analyze numerically and analytically beyond the classical limit, addressing observable dynamics, phenomenology in different (laboratory and rotating) frames, Liouvillian spectral features, and quantum fluctuations. Via an effective semiclassical description, we show that phase diffusion dominates in the incommensurate time crystal (or continuous time crystal in the rotating frame), which manifests as a band of eigenmodes with a lifetime growing linearly with the mean-field excitation number. Instead, in the discrete time-crystal phase, the leading fluctuation process corresponds to quantum activation with a single mode that has an exponentially growing lifetime. Interestingly, the transition between these two regimes manifests itself already in the quantum regime as a spectral singularity, namely, as an exceptional point mediating between phase diffusion and quantum activation. Finally, we discuss this transition between different time-crystal orders in the context of synchronization phenomena. Published by the American Physical Society 2024

Multicritical dissipative phase transitions in the anisotropic open quantum Rabi model

We investigate the nonequilibrium steady state of the anisotropic open quantum Rabi model, which exhibits first-order and second-order dissipative phase transitions upon varying the degree of anisotropy between the coupling strengths of rotating and counter-rotating terms. Using both semiclassical and quantum approaches, we find a rich phase diagram resulting from the interplay between the anisotropy and the dissipation. First, there exists a bistable phase where both the normal and superradiant phases are stable. Second, there are multicritical points where the phase boundaries for the first- and second-order phase transitions meet. We show that a new set of critical exponents governs the scaling of the multicritical points. Finally, we discuss the feasibility of observing the multicritical transitions and bistability using a pair of trapped ions where the anisotropy can be tuned by controlling the intensity of the Raman transitions. Our study enlarges the scope of critical phenomena that may occur in finite-component quantum systems, which could be useful for applications in critical quantum sensing. Published by the American Physical Society 2024

Dynamic hysteresis across a dissipative multi-mode phase transition

Dynamic hysteresis across a dissipative multi-mode phase transition

Successive quasienergy collapse and breakdown of photon blockade in the few-emitter limit

The emergent behavior that arises in many-body systems of increasing size follows universal laws that become apparent in order-to-disorder transitions. While this behavior has been traditionally studied for large numbers of emitters, recent progress allows for the exploration of the few-emitter limit, where correlations can be measured and connected to microscopic models to gain further insight into order-to-disorder transitions. We explore this few-body limit in the driven and damped Tavis–Cummings model, which describes a collection of atoms interacting with a driven and damped cavity mode. Our exploration revolves around the dressed states of the atomic ensemble and field, whose energies are shown to collapse as the driving field is increased to mark the onset of a dissipative quantum phase transition. The collapse occurs in stages and is an effect of light-matter correlations that are overlooked for single atoms and neglected in mean-field models. The implications of these correlations over the macroscopic observables of the system are presented. We encounter a shift in the expected transition point and an increased number of parity-broken states to choose from once the ordered phase is reached.

Time Crystal in a Single-Mode Nonlinear Cavity.

Time crystal is a class of nonequilibrium phases with broken time-translational symmetry. Here, we demonstrate the time crystal in a single-mode nonlinear cavity. The time crystal originates from the self-oscillation induced by a linear gain and is stabilized by a nonlinear damping. We show in the time crystal phase there are sharp dissipative gap closing and pure imaginary eigenvalues of the Liouvillian spectrum in the thermodynamic limit. Dynamically, we observe a metastable regime with the emergence of quantum oscillation, followed by a dissipative evolution with a timescale much longer than the oscillating period. Moreover, we show there is a dissipative phase transition at the Hopf bifurcation, which can be characterized by the photon number fluctuation in the steady state. These results pave a new promising way for further experiments and deepen our understanding of time crystals.

Inelastic Decay from Integrability

A hallmark of integrable systems is the purely elastic scattering of their excitations. Such systems possess an extensive number of locally conserved charges, leading to the conservation of the number of scattered excitations, as well as their set of individual momenta. In this work, we show that inelastic decay can nevertheless be observed in circuit-QED realizations of integrable boundary models. We consider the scattering of microwave photons off impurities in superconducting circuits implementing the boundary sine-Gordon and Kondo models, which are both integrable. We show that not only is inelastic decay possible for the microwave photons, in spite of integrability, and due to a nonlinear relation between them and the elastically scattered excitations, but also that integrability in fact provides powerful analytical tools allowing us to obtain exact expressions for response functions describing the inelastic decay. Using the framework of form factors, we calculate the total inelastic decay rate and elastic phase shift of the microwave photons, extracted from a two-point response function. We then go beyond linear response and obtain the exact energy-resolved inelastic decay spectrum, using a novel method to evaluate form-factor expansions of three-point response functions, which could prove useful in other applications of integrable quantum field theories. Our results could be relevant to several recent photon-splitting experiments and, in particular, to recent experimental works that provide evidence for the elusive Schmid-Bulgadaev dissipative quantum phase transition. Published by the American Physical Society 2024

Dissipative stability and dynamical phase transition in two driven interacting qubits

We examine a two-qubit system influenced by a time-periodic external field while interacting with a Markovian bath. This scenario significantly impacts the temporal coherence characteristics of the system. By solving the evolution equation for the density matrix operator, we determine the characteristic equilibration time and analyze the concurrence parameter-a key metric for quantifying entanglement. Our findings reveal the system’s ability to navigate through a dynamic phase transition. These results pave the way to designing systems of interacting qubits demonstrating robust entanglement under realistic conditions of interaction with the environment.

Quantum Entangled States of a Classically Radiating Macroscopic Spin

Entanglement constitutes a main feature that distinguishes quantum from classical physics. Here, however, we show that entanglement may also serve as the essential ingredient for the emergence of classical behavior in a radiating spin system. We consider the relation between the state of a macroscopic spin, such as an atomic ensemble, and the radiation it emits. We introduce a new class of macroscopic spin states, the coherently radiating spin states (CRSSs), defined as the asymptotic eigenstates of the SU(2) lowering operator. We find that a spin emitter in a CRSS radiates classical coherent light, although the CRSS itself is a quantum entangled state exhibiting spin squeezing. We further show that the CRSS is naturally realized in Dicke superradiance and underlies the dissipative Dicke phase transition, hence predicting the optimal scaling of spin squeezing in superradiance. More generally, the CRSS emerges as the ground state of a collective spin Hamiltonian. The CRSS thus provides a promising concept for studying many-body spin systems in various platforms, with applications ranging from quantum metrology and lasing to phase transitions. Published by the American Physical Society 2024

Dissipative phase transitions in n-photon driven quantum nonlinear resonators

We investigate and characterize the emergence of finite-component dissipative phase transitions (DPTs) in nonlinear photon resonators subject to n-photon driving and dissipation. Exploiting a semiclassical approach, we derive general results on the occurrence of second-order DPTs in this class of systems. We show that for all odd n, no second-order DPT can occur while, for even n, the competition between higher-order nonlinearities determines the nature of the criticality and allows for second-order DPTs to emerge only for n=2 and n=4. As pivotal examples, we study the full quantum dynamics of three- and four-photon driven-dissipative Kerr resonators, confirming the prediction of the semiclassical analysis on the nature of the transitions. The stability of the vacuum and the typical timescales needed to access the different phases are also discussed. We also show a first-order DPT where multiple solutions emerge around zero, low, and high-photon numbers. Our results highlight the crucial role played by strong and weak symmetries in triggering critical behaviors, providing a Liouvillian framework to study the effects of high-order nonlinear processes in driven-dissipative systems, that can be applied to problems in quantum sensing and information processing.

A quantum battery with quadratic driving

Quantum batteries are energy storage devices built using quantum mechanical objects, which are developed with the aim of outperforming their classical counterparts. Proposing optimal designs of quantum batteries which are able to exploit quantum advantages requires balancing the competing demands for fast charging, durable storage and effective work extraction. Here we study theoretically a bipartite quantum battery model, composed of a driven charger connected to an energy holder, within two paradigmatic cases of a driven-dissipative open quantum system: linear driving and quadratic driving. The linear battery is governed by a single exceptional point which splits the response of the battery into two regimes, one of which induces a good amount of useful work. Quadratic driving leads to a squeezed quantum battery, which generates plentiful useful work near to critical points associated with dissipative phase transitions. Our theoretical results may be realized with parametric cavities or nonlinear circuits, potentially leading to the manifestation of a quantum battery exhibiting squeezing.

Quantum metrology with boundary time crystals

Quantum sensing is one of the arenas that exemplifies the superiority of quantum technologies over their classical counterparts. Such superiority, however, can be diminished due to unavoidable noise and decoherence of the probe. Thus, metrological strategies to fight against or profit from decoherence are highly desirable. This is the case of certain types of decoherence-driven many-body systems supporting dissipative phase transitions, which might be helpful for sensing. Boundary time crystals are exotic dissipative phases of matter in which the time-translational symmetry is broken, and long-lasting oscillations emerge in open quantum systems at the thermodynamic limit. We show that the transition from a symmetry unbroken into a boundary time crystal phase, described by a second-order transition, reveals quantum-enhanced sensitivity quantified through quantum Fisher information. We also determine the critical exponents of the system and establish their relationship. Our scheme is indeed a demonstration of harnessing decoherence for achieving quantum-enhanced sensitivity. From a practical perspective, it has the advantage of being independent of initialization and can be captured by a simple measurement.

Neglected U(1) phase in the Schrödinger representation of quantum mechanics and particle number conserving formalisms for superconductivity

Superconductivity is reformulated as a phenomenon in which a stable velocity field is created by a U(1) phase neglected by Dirac in the Schrödinger representation of quantum mechanics. The neglected phase gives rise to a U(1) gauge field expressed as the Berry connection from many-body wave functions. The inclusion of this gauge field transforms the standard particle-number non-conserving formalism of superconductivity to a particle-number conserving one with many results of the former unaltered. In other words, the new formalism indicates that the current standard one is an approximation that effectively takes into account this neglected U(1) gauge field by employing the particle-number non-conserving formalism. Since the standard and new formalisms are physically different, conflicting results are predicted in some cases. We reexamine the Josephson relation and show that a capacitance contribution of the Josephson junction to the U(1) phase is missing in the standard formalism, and inclusion of it indicates that the standard theory actually does not agree with the experiment while the new one does. It is also shown that the dissipative quantum phase transition in Josephson junctions predicted in the standard theory does not exist in the new one in accordance with a recent experiment (Murani et al 2020 Phys. Rev. X 10 021003).

Bidirectionally Modulating the Dissipative Phase Transition of UCST Polymers in a Programmable Manner Using Visible Light

AbstractDynamic phase transitions are important in living organisms for sustaining their adaptive structures and functions. The design of artificial dynamic systems using light as a noninvasive input fuel has gained significant interest to mimic such adaptive features. Here the development of light‐fueled dissipative phase transitions of upper critical solution temperature polymers by introducing pendant spiropyrans as photoactive units, is reported. The reversible open‐close photoisomerization of spiropyrans is designed to undergo either an enhancement or a decline of their net charge, which is subsequently used to regulate the electrostatic interactions between polymer chains, and ultimately shift their phase transition temperatures to either a lower or a higher direction. The degree and speed of such bidirectional shifting are flexibly modulated by manipulating the external illumination parameters or varying the compositions/concentrations of the polymers. The diametrically opposite transmittance changes driven by light are utilized to produce a series of complementary patterns and shapes for application in transient information storage and encryption with improved accuracy and security. This work offers a bidirectional spatiotemporal modulation of dissipative phase transitions of polymers using visible light that allows highly tunable and adaptable features shared with their natural counterparts.

Numerical variational studies of quantum phase transitions in the sub-Ohmic spin-boson model with multiple polaron ansatz

With extensive variational calculations, dissipative quantum phase transitions in the sub-Ohmic spin-boson model are numerically studied in a dense limit of environmental modes. By employing a generalized trial wave function composed of coherent-state expansions, transition points and critical exponents are accurately determined for various spectral exponents, demonstrating excellent agreement with those obtained by other sophisticated numerical techniques. Besides, the quantum-to-classical correspondence is fully confirmed over the entire sub-Ohmic range, compared with theoretical predictions of the long-range Ising model. Mean-field and non-mean-field critical behaviors are found in the deep and shallow sub-Ohmic regimes, respectively, and distinct physical mechanisms of them are uncovered.

Natural exceptional points in the excitation spectrum of a light–matter system

In this work, we observe natural exceptional points in the excitation spectrum of an exciton–polariton system by optically tuning the light–matter interactions. The observed exceptional points do not require any spatial or polarization degrees of freedom and result solely from the transition from weak to strong light–matter coupling. It was demonstrated that they do not coincide with the threshold for photon lasing, confirming previous theoretical predictions [Phys. Rev. Lett. 122, 185301 (2019)PRLTAO0031-900710.1103/PhysRevLett.122.185301, Optica 7, 1015 (2020)OPTIC82334-253610.1364/OPTICA.397378]. Using a technique where a strong coherent laser pump induces up-converted excitations, we encircle the exceptional point in the parameter space of coupling strength and particle momentum. Our method of local optical control of light–matter coupling paves the way to the investigation of fundamental phenomena, including dissipative phase transitions and non-Hermitian topological states.

Quantum metrology with critical driven-dissipative collective spin system

We propose two critical dissipative quantum metrology schemes for single parameter estimation which are based on a quantum probe consisting of a coherently driven ensemble of N spin-1/2 particles under the effect of a collective spin decay. The collective spin system exhibits a dissipative phase transition between thermal and ferromagnetic phases, which is characterized by a nonanalytical behavior of the spin observables. We show that thanks to the dissipative phase transition the sensitivity of the parameter estimation can be significantly enhanced. Furthermore, we show that our steady state is a spin squeezed state which allows one to perform parameter estimation with sub shot-noise limited measurement uncertainty.

Parametrically driving a quantum oscillator into exceptionality

The mathematical objects employed in physical theories do not always behave well. Einstein’s theory of space and time allows for spacetime singularities and Van Hove singularities arise in condensed matter physics, while intensity, phase and polarization singularities pervade wave physics. Within dissipative systems governed by matrices, singularities occur at the exceptional points in parameter space whereby some eigenvalues and eigenvectors coalesce simultaneously. However, the nature of exceptional points arising in quantum systems described within an open quantum systems approach has been much less studied. Here we consider a quantum oscillator driven parametrically and subject to loss. This squeezed system exhibits an exceptional point in the dynamical equations describing its first and second moments, which acts as a borderland between two phases with distinctive physical consequences. In particular, we discuss how the populations, correlations, squeezed quadratures and optical spectra crucially depend on being above or below the exceptional point. We also remark upon the presence of a dissipative phase transition at a critical point, which is associated with the closing of the Liouvillian gap. Our results invite the experimental probing of quantum resonators under two-photon driving, and perhaps a reappraisal of exceptional and critical points within dissipative quantum systems more generally.