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arXiv:1808.00726 · Physical Review A

Catching and reversing quantum jumps and thermodynamics of quantum trajectories

Juan P. Garrahan, Mădălin Guţǎ

Published Nov 29, 2018• 18 citations
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Abstract

A recent experiment by Minev et al., arXiv:1803.00545 demonstrated that in a dissipative (artificial) three-level atom with strongly intermittent dynamics it is possible to ``catch and reverse'' a quantum jump ``midflight'': by the conditional application of a unitary perturbation after a fixed time with no jumps, the system was prevented from getting shelved in the dark state, thus removing the intermittency from the dynamics. Here we offer an interpretation of this phenomenon in terms of the dynamical large deviation formalism for open quantum dynamics. In this approach, intermittency is seen as the first-order coexistence of active and inactive dynamical phases (or more precisely, dynamical regimes in this finite level system). Dark periods are thus like time bubbles of the inactive regime in the active one. Here we consider a controlled dynamics via the (single---as in the experiment---or multiple) application of a unitary control pulse during no-jump periods. By considering the large deviation statistics of the emissions, we show that appropriate choice of the control allows one to stabilize a desired dynamical regime and remove the intermittency. In the thermodynamic analogy, the effect of the control is to prick bubbles, thus preventing the fluctuations that manifest phase coexistence. We discuss similar controlled dynamics in broader settings.

DOI
10.1103/physreva.98.052137

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A recent experiment by Minev et al., arXiv:1803.00545 demonstrated that in a dissipative (artificial) three-level atom with strongly intermittent dynamics it is possible to catch and reverse'' a quantum jump midflight'': by the conditional application of a unitary perturbation after a fixed time with no jumps, the system was prevented from getting shelved in the dark state, thus removing the intermittency from the dynamics. Here we offer an interpretation of this phenomenon in terms of the dynamical large deviation formalism for open quantum dynamics. In this approach, intermittency is seen as the first-order coexistence of active and inactive dynamical phases (or more precisely, dynamical regimes in this finite level system). Dark periods are thus like time bubbles of the inactive regime in the active one. Here we consider a controlled dynamics via the (single---as in the experiment---or multiple) application of a unitary control pulse during no-jump periods. By considering the large deviation statistics of the emissions, we show that appropriate choice of the control allows one to stabilize a desired dynamical regime and remove the intermittency. In the thermodynamic analogy, the effect of the control is to prick bubbles, thus preventing the fluctuations that manifest phase coexistence. We discuss similar controlled dynamics in broader settings.
We apply the large-deviation method to study trajectories in dissipative quantum systems. We show that in the long time limit the statistics of quantum jumps can be understood from thermodynamic arguments in terms of dynamical phases and transitions between them in trajectory space. We illustrate our approach with three simple examples: a driven 2-level system where we find a particular scale invariance point in the ensemble of trajectories of emitted photons; a blinking 3-level system, where we argue that intermittency in the photon count is related to a crossover between distinct dynamical phases; and a micromaser, where we find an actual first-order phase transition in the ensemble of trajectories.
We consider Markovian open quantum systems subject to stochastic resetting, which means that the dissipative time evolution is reset at randomly distributed times to the initial state. We show that the ensuing dynamics is non-Markovian and has the form of a generalized Lindblad equation. Interestingly, the statistics of quantum-jumps can be exactly derived. This is achieved by combining techniques from the thermodynamics of quantum-jump trajectories with the renewal structure of the resetting dynamics. We consider as an application of our analysis a driven two-level and an intermittent three-level system. Our findings show that stochastic resetting may be exploited as a tool to tailor the statistics of the quantum-jump trajectories and the dynamical phases of open quantum systems.
We consider Markovian open quantum systems subject to stochastic resetting, which means that the dissipative time evolution is reset at randomly distributed times to the initial state. We show that the ensuing dynamics is non-Markovian and has the form of a generalized Lindblad equation. Interestingly, the statistics of quantum-jumps can be exactly derived. This is achieved by combining techniques from the thermodynamics of quantum-jump trajectories with the renewal structure of the resetting dynamics. We consider as an application of our analysis a driven two-level and an intermittent three-level system. Our findings show that stochastic resetting may be exploited as a tool to tailor the statistics of the quantum-jump trajectories and the dynamical phases of open quantum systems.
Large dynamical fluctuations---atypical realizations of the dynamics sustained over long periods of time---can play a fundamental role in determining the properties of collective behavior of both classical and quantum nonequilibrium systems. Rare dynamical fluctuations, however, occur with a probability that often decays exponentially in their time extent, thus making them difficult to be directly observed and exploited in experiments. Here, using methods from dynamical large deviations, we explain how rare dynamics of a given (Markovian) open quantum system can always be obtained from the typical realizations of an alternative (also Markovian) system. The correspondence between these two sets of realizations can be used to engineer and control open quantum systems with a desired statistics ``on demand.'' We illustrate these ideas by studying the photon emission behavior of a three-qubit system which displays a sharp dynamical crossover between active and inactive dynamical phases.
Quantum physics was invented to account for two fundamental features of measurement results their discreetness and randomness. Emblematic of these features is the Bohr idea of quantum jumps between two discrete energy levels of an atom. Experimentally, quantum jumps were first observed in an atomic ion driven by a weak deterministic force while under strong continuous energy measurement. The times at which the discontinuous jump transitions occur are reputed to be fundamentally unpredictable. Can there be, despite the indeterminism of quantum physics, a possibility to know if a quantum jump is about to occur or not? Here, we answer this question affirmatively by experimentally demonstrating that the jump from the ground to an excited state of a superconducting artificial three-level atom can be tracked as it follows a predictable flight, by monitoring the population of an auxiliary energy level coupled to the ground state. The experimental results demonstrate that the jump evolution when completed is continuous, coherent, and deterministic. Furthermore, exploiting these features and using real-time monitoring and feedback, we catch and reverse a quantum jump mid-flight, thus deterministically preventing its completion. Our results, which agree with theoretical predictions essentially without adjustable parameters, support the modern quantum trajectory theory and provide new ground for the exploration of real-time intervention techniques in the control of quantum systems, such as early detection of error syndromes.
In Nature, 570, 200 (2019), Minev and co-authors’ experiment shows how to deterministically “catch and reverse a quantum jump mid-flight” in a continuously-observed Rabi-stimulated qubit. Its interpretation is in debate (La Recherche, 555, 40, (2020)). We show that the quantum Zeno effect (QZE) of continuous measurement —by use of photon emission from a 3rd high-rate monitored ancilla level— can be described by an action-angle canonical transformation of the original Hamiltonian dynamical system (HDS) theory of QZE. Then energy whose mean value yields the well-known resonant Rabi harmonic dynamics is actually defined by large-amplitude high-frequency oscillations of the internal as well as of the overall phase of the two-level system. By making use of their standard deviation, we show that the separatrix crossing of the HDS trajectory yields the quantized action nh where n = 1, 2, 3 .... Therefore, the jump dynamics observed in Minev et al. experiment belongs to a series of discrete quantum jumps: it corresponds in this experiment to n = 3.