We analyze the quantum trajectory dynamics of free fermions subject to continuous monitoring. For weak monitoring, we identify a novel dynamical regime of subextensive entanglement growth, ...reminiscent of a critical phase with an emergent conformal invariance. For strong monitoring, however, the dynamics favors a transition into a quantum Zeno-like area-law regime. Close to the critical point, we observe logarithmic finite size corrections, indicating a Berezinskii-Kosterlitz-Thouless mechanism underlying the transition. This uncovers an unconventional entanglement transition in an elementary, physically realistic model for weak continuous measurements. In addition, we demonstrate that the measurement aspect in the dynamics is crucial for whether or not a phase transition takes place.
We identify an unconventional algebraic scaling phase in the quantum dynamics of long-range hopping, free fermions, which are exposed to continuous local measurements. The algebraic phase occurs for ...hopping decay exponents 1<p≲3/2, and features an algebraic entanglement entropy growth, and a slow algebraic decay of the density-density correlation function, both with a fractional exponent. It is separated from a critical phase with logarithmic entanglement growth at small, and an area law phase with constant entanglement entropy at large monitoring rates. A perturbative renormalization group analysis predicts that the transitions to the long-range phase correspond to an unconventional, modified sine-Gordon theory. Exact numerical simulations of the monitored wave functions are in excellent agreement with an analytical replica field theory approach, which confirms the view of the measurement-induced phase transition as a quantum phase transition in the dark state of an effective, non-Hermitian Hamiltonian.
A wave function subject to unitary time evolution and exposed to measurements undergoes pure state dynamics, with deterministic unitary and probabilistic measurement-induced state updates, defining a ...quantum trajectory. For many-particle systems, the competition of these different elements of dynamics can give rise to a scenario similar to quantum phase transitions. To access this competition despite the randomness of single quantum trajectories, we construct ann-replica Keldysh field theory for the ensemble average of thenth moment of the trajectory projector. A key finding is that this field theory decouples into one set of degrees of freedom that heats up indefinitely, whilen−1others can be cast into the form of pure state evolutions generated by an effective non-Hermitian Hamiltonian. This decoupling is exact for free theories, and useful for interacting ones. In particular, we study locally measured Dirac fermions in (1+1) dimensions, which can be bosonized to a monitored interacting Luttinger liquid at long wavelengths. For this model, the non-Hermitian Hamiltonian corresponds to a quantum sine-Gordon model with complex coefficients. A renormalization group analysis reveals a gapless critical phase with logarithmic entanglement entropy growth, and a gapped area law phase, separated by a Berezinskii-Kosterlitz-Thouless transition. The physical picture emerging here is a measurement-induced pinning of the trajectory wave function into eigenstates of the measurement operators, which succeeds upon increasing the monitoring rate across a critical threshold.
We present an analog of the phenomenon of orthogonality catastrophe in quantum many-body systems subject to a local dissipative impurity. We show that the fidelity F(t), giving a measure for distance ...of the time-evolved state from the initial one, displays a universal scaling form F(t)∝t^{θ}e^{-γt}, when the system supports long-range correlations, in a fashion reminiscent of traditional instances of orthogonality catastrophe in condensed matter. An exponential falloff at rate γ signals the onset of environmental decoherence, which is critically slowed down by the additional algebraic contribution to the fidelity. This picture is derived within a second-order cumulant expansion suited for Liouvillian dynamics, and substantiated for the one-dimensional transverse field quantum Ising model subject to a local dephasing jump operator, as well as for XY and XX quantum spin chains, and for the two-dimensional Bose gas deep in the superfluid phase with local particle heating. Our results hint that local sources of dissipation can be used to inspect real-time correlations and to induce a delay of decoherence in open quantum many-body systems.
Self-organized criticality is an elegant explanation of how complex structures emerge and persist throughout nature
, and why such structures often exhibit similar scale-invariant properties
. ...Although self-organized criticality is sometimes captured by simple models that feature a critical point as an attractor for the dynamics
, the connection to real-world systems is exceptionally hard to test quantitatively
. Here we observe three key signatures of self-organized criticality in the dynamics of a driven-dissipative gas of ultracold potassium atoms: self-organization to a stationary state that is largely independent of the initial conditions; scale-invariance of the final density characterized by a unique scaling function; and large fluctuations of the number of excited atoms (avalanches) obeying a characteristic power-law distribution. This work establishes a well-controlled platform for investigating self-organization phenomena and non-equilibrium criticality, with experimental access to the underlying microscopic details of the system.
We explore the nature of the Bose condensation transition in driven open quantum systems, such as exciton-polariton condensates. Using a functional renormalization group approach formulated in the ...Keldysh framework, we characterize the dynamical critical behavior that governs decoherence and an effective thermalization of the low frequency dynamics. We identify a critical exponent special to the driven system, showing that it defines a new dynamical universality class. Hence critical points in driven systems lie beyond the standard classification of equilibrium dynamical phase transitions. We show how the new critical exponent can be probed in experiments with driven cold atomic systems and exciton-polariton condensates.
Topology by dissipation Bardyn, C-E; Baranov, M A; Kraus, C V ...
New journal of physics,
08/2013, Letnik:
15, Številka:
8
Journal Article
Recenzirano
Odprti dostop
Topological states of fermionic matter can be induced by means of a suitably engineered dissipative dynamics. Dissipation then does not occur as a perturbation, but rather as the main resource for ...many-body dynamics, providing a targeted cooling into topological phases starting from arbitrary initial states. We explore the concept of topological order in this setting, developing and applying a general theoretical framework based on the system density matrix that replaces the wave function appropriate for the discussion of Hamiltonian ground-state physics. We identify key analogies and differences to the more conventional Hamiltonian scenario. Differences essentially arise from the fact that the properties of the spectrum and of the state of the system are not as tightly related as in the Hamiltonian context. We provide a symmetry-based topological classification of bulk steady states and identify the classes that are achievable by means of quasi-local dissipative processes driving into superfluid paired states. We also explore the fate of the bulk-edge correspondence in the dissipative setting and demonstrate the emergence of Majorana edge modes. We illustrate our findings in one- and two-dimensional models that are experimentally realistic in the context of cold atoms.
We show how engineered classical noise can be used to generate constrained Hamiltonian dynamics in atomic quantum simulators of many-body systems, taking advantage of the continuous Zeno effect. ...After discussing the general theoretical framework, we focus on applications in the context of lattice gauge theories, where imposing exotic, quasilocal constraints is usually challenging. We demonstrate the effectiveness of the scheme for both Abelian and non-Abelian gauge theories, and discuss how engineering dissipative constraints substitutes complicated, nonlocal interaction patterns by global coupling to laser fields.
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