We show that applying feedback and weak measurements to a quantum system induces phase transitions beyond the dissipative ones. Feedback enables controlling essentially quantum properties of the transition, i.e., its critical exponent, as it is driven by the fundamental quantum fluctuations due to measurement. Feedback provides the non-Markovianity and nonlinearity to the hybrid quantum-classical system, and enables simulating effects similar to spin-bath problems and Floquet time crystals with tunable long-range (long-memory) interactions.
We show that applying feedback and weak measurements to a quantum system induces phase transitions beyond the dissipative ones. Feedback enables controlling essentially quantum properties of the transition, i.e., its critical exponent, as it is driven by the fundamental quantum fluctuations due to measurement. Feedback provides the non-Markovianity and nonlinearity to the hybrid quantum-classical system, and enables simulating effects similar to spin-bath problems and Floquet time crystals with tunable long-range (long-memory) interactions.
We shift the paradigm of feedback control from the control of quantum states to the control of phase transitions in quantum systems. We show that feedback allows tuning the universality class of phase transitions via modifying its critical exponent. We expand our previous treatment [Ivanov et al., Phys. Rev. Lett. 124, 010603 (2020)] of the Dicke model and go beyond the approximation of the adiabatically eliminated light field. Both linearized and nonlinear models of spin ensembles are considered. The tunability of quantum fluctuations near the critical point by the feedbacks of nontrivial shapes is explained by considering the fluctuation spectra and the system behavior at single quantum trajectories.
We find that feedback control may induce ``pseudo''-nonlinear dynamics in a damped harmonic oscillator, whose centroid trajectory in the phase space behaves like a classical nonlinear system. Thus, similar to nonlinear amplifiers (e.g., rf-driven Josephson junctions), feedback control on the harmonic oscillator can induce nonlinear bifurcation, which can be used to amplify small signals and further to measure quantum states of qubits. Using the cavity QED and the circuit QED systems as examples, we show how to apply our method to measuring the states of two-level atoms and superconducting charge qubits.
The problem of optimal control of non-Markovian open quantum system via weak measurement is presented. Based on the non-Markovian master equation, we evaluate exactly the non-Markovian effect on the dynamics of the system of interest interacting with a dissipative reservoir. We find that the non-Markovian reservoir has dual effects on the system: dissipation and backaction. The dissipation exhausts the coherence of the quantum system, whereas the backaction revives it. Moreover, we design the control Hamiltonian with the control laws attained by the stochastic optimal control and the corresponding optimal principle. At last, we considered the exact decoherence dynamics of a qubit in a dissipative reservoir composed of harmonic oscillators, and demonstrated the effectiveness of our optimal control strategy. Simulation results showed that the coherence will completely lost in the absence of control neither in non-Markovian nor Markovian system. However, the optimal feedback control steers it to a stationary stochastic process which fluctuates around the target. In this case the decoherence can be controlled effectively, which indicates that the engineered artificial reservoirs with optimal feedback control may be designed to protect the quantum coherence in quantum information and quantum computation.
Abstract Non-equilibrium phase transitions are a vibrant frontier in physics, driving breakthroughs across diverse disciplines in recent years. Thermal spin ensembles, a captivating many-body quantum system, have harnessed their collective strengths to set remarkable measurement benchmarks in equilibrium. However, their non-equilibrium dynamics remain unexplored, with nonlinear interactions among constituents offering a rich playground for phase transition studies. Here, we employ nonlinear magnetic feedback to achieve real-time observation and control of phase transitions in a driven-dissipative spin ensemble, unveiling dynamic shifts between limit cycles, subharmonics, and chaos. This work not only deepens our grasp of critical phenomena in non-equilibrium systems but also paves the way for chaos-based sensing and information processing technologies, bridging fundamental physics with transformative applications.
Monitored quantum circuits in which entangling unitary dynamics compete with projective local measurements can host measurement-induced phase transitions witnessed by entanglement measures at late times. Adding feedback conditioned on the measurement outcomes gives rise to another type of phase transition witnessed by local order parameters and correlation functions. These transitions, known as control or absorbing-state transitions, generically occur within the area-law entanglement phase and are thought to be governed by classical physics in that their critical exponents match those of the classical limit of the model. In this work, we examine quantum features of these transitions, focusing on a Bernoulli circuit model with a well-defined classical limit, in the presence of unitary dynamics, measurements, and feedback. First we demonstrate that, in the local basis defined by the absorbing state, the steady-state quantum coherence undergoes a phase transition at the control transition, where its logarithm changes discontinuously from volume- to area-law scaling. Second, we analyze the control transition from the perspective of fluctuations in observables, which carry two contributions: classical fluctuations over circuit realizations (present in the classical limit), and quantum fluctuations over trajectories and states (both absent in the classical limit). Both contributions can be estimated in experiments without post-selection. The circuit-to-circuit fluctuations, the dominant contribution, carry the critical behavior of the classical limit. However, the subleading quantum fluctuations that represent fluctuations between different quantum ``worlds'' also go critical at the control transition. These critical quantum fluctuations at the control transition also occur in other models, and we discuss how they can be measured experimentally without post-selection.
The environmental interaction is a fundamental consideration in any controlled quantum system. While an interaction with a dissipative bath can lead to decoherence, it can also provide desirable emergent effects including induced spin-spin correlations. In this Letter, we show that under quite general conditions, a dissipative bosonic bath can induce a long-range ordered phase, without the inclusion of any additional direct spin-spin couplings. Through a quantum-to-classical mapping and classical Monte Carlo simulation, we investigate the T=0 quantum phase transition of an Ising chain embedded in a bosonic bath with Ohmic dissipation. We show that the quantum critical point is continuous, Lorentz invariant with a dynamical critical exponent z=1.07(9), has a correlation length exponent $\ensuremath{\nu}=0.80(5)$, and anomalous exponent $\ensuremath{\eta}=1.02(6)$, thus the universality class is distinct from the previously studied limiting cases. The implications of our results on experiments in ultracold atomic mixtures and qubit chains in dissipative environments are discussed.