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Register a new userDynamical purification phase transitions induced by quantum measurements
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Continuously monitoring the environment of a quantum many-body system reduces the entropy of (purifies) the reduced density matrix of the system, conditional on the outcomes of the measurements. We show that, for mixed initial states, a balanced competition between measurements and entangling interactions within the system can result in a dynamical purification phase transition between (i) a phase that locally purifies at a constant system-size-independent rate, and (ii) a mixed phase where the purification time diverges exponentially in the system size. The residual entropy density in the mixed phase implies the existence of a quantum error-protected subspace where quantum information is reliably encoded against the future non-unitary evolution of the system. We show that these codes are of potential relevance to fault-tolerant quantum computation as they are often highly degenerate and satisfy optimal tradeoffs between encoded information densities and error thresholds. In spatially local models in 1+1 dimensions, this phase transition for mixed initial states occurs concurrently with a recently identified class of entanglement phase transitions for pure initial states. The mutual information of an initially completely-mixed state in 1+1 dimensions grows sublinearly in time due to the formation of the error protected subspace. The purification transition studied here also generalizes to systems with long-range interactions, where conventional notions of entanglement transitions have to be reformulated. Purification dynamics is likely a more robust probe of the transition in experiments, where imperfections generically reduce entanglement and drive the system towards mixed states. We describe the motivations for studying this novel class of non-equilibrium quantum dynamics in the context of advanced quantum computing platforms and fault-tolerant quantum computation.
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The quantum critical detector (QCD), recently introduced for weak-signal amplification [Opt. Express 27, 10482 (2019)], functions by exploiting high sensitivity near the phase transition point of first-order quantum phase transitions. We contrast the behavior of the first-order as well as the second-order quantum phase transitions (QPTs) in the detector. We find that the giant sensitivity to a weak input signal, which can be utilized for quantum amplification, only exists in first-order QPTs. We define two new magnetic order parameters to quantitatively characterize the first-order QPT of the interacting spins in the detector. We also introduce the Husimi $Q$-functions as a powerful tool to show the fundamental change in the ground-state wave function of the detector during the QPTs and especially, the intrinsic dynamical change within the detector during a quantum critical amplification. We explicitly show the high figures of merit of the QCD via the quantum gain and signal-to-quantum noise ratio. Specifically, we predict the existence of a universal first-order QPT in the interacting spin system resulting from two competing ferromagnetic orders. Our results motivate new designs of weak signal detectors by engineering first-order QPTs, which are of fundamental significance in the search for new particles, quantum metrology, and information science.
We introduce a first-order quantum-phase-transition model, which exhibits giant sensitivity $chi propto N^2$ at the critical point. Exploiting this effect, we propose a quantum critical detector (QCD) to amplify weak input signals. The time-dynamic QCD functions by triggering a first-order dynamical quantum phase transition in a system of spins with long-range interactions coupled to a bosonic mode. We numerically demonstrate features of the dynamical quantum phase transition, which leads to a time-dependent quantum gain. We also show the linear scaling with the spin number $N$ in both the quantum gain and the corresponding signal-to-quantum noise ratio of this QCD. Our QCD can be a resource for metrology, weak signal amplification, and single photon detection.
Considering nonintegrable quantum Ising chains with exponentially decaying interactions, we present matrix product state results that establish a connection between low-energy quasiparticle excitations and the kind of nonanalyticities in the Loschmidt return rate. When domain walls in the spectrum of the quench Hamiltonian are energetically favored to be bound rather than freely propagating, anomalous cusps appear in the return rate regardless of the initial state. In the nearest-neighbor limit, domain walls are always freely propagating, and anomalous cusps never appear. As a consequence, our work illustrates that models in the same equilibrium universality class can still exhibit fundamentally distinct out-of-equilibrium criticality. Our results are accessible to current ultracold-atom and ion-trap experiments.
Dynamical quantum phase transitions (DQPTs) represent a counterpart in non-equilibrium quantum time evolution of thermal phase transitions at equilibrium, where real time becomes analogous to a control parameter such as temperature. In quenched quantum systems, recently the occurrence of DQPTs has been demonstrated, both with theory and experiment, to be intimately connected to changes of topological properties. Here, we contribute to broadening the systematic understanding of this relation between topology and DQPTs to multi-orbital and disordered systems. Specifically, we provide a detailed ergodicity analysis to derive criteria for DQPTs in all spatial dimensions, and construct basic counter-examples to the occurrence of DQPTs in multi-band topological insulator models. As a numerical case study illustrating our results, we report on microscopic simulations of the quench dynamics in the Harper-Hofstadter model. Furthermore, going gradually from multi-band to disordered systems, we approach random disorder by increasing the (super) unit cell within which random perturbations are switched on adiabatically. This leads to an intriguing order of limits problem which we address by extensive numerical calculations on quenched one-dimensional topological insulators and superconductors with disorder.
Dynamical phase transitions extend the notion of criticality to non-stationary settings and are characterized by sudden changes in the macroscopic properties of time-evolving quantum systems. Investigations of dynamical phase transitions combine aspects of symmetry, topology, and non-equilibrium physics, however, progress has been hindered by the notorious difficulties of predicting the time evolution of large, interacting quantum systems. Here, we tackle this outstanding problem by determining the critical times of interacting many-body systems after a quench using Loschmidt cumulants. Specifically, we investigate dynamical topological phase transitions in the interacting Kitaev chain and in the spin-1 Heisenberg chain. To this end, we map out the thermodynamic lines of complex times, where the Loschmidt amplitude vanishes, and identify the intersections with the imaginary axis, which yield the real critical times after a quench. For the Kitaev chain, we can accurately predict how the critical behavior is affected by strong interactions, which gradually shift the time at which a dynamical phase transition occurs. Our work demonstrates that Loschmidt cumulants are a powerful tool to unravel the far-from-equilibrium dynamics of strongly correlated many-body systems, and our approach can immediately be applied in higher dimensions.
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