Catching and reversing quantum jumps and thermodynamics of quantum trajectories

Juan P. Garrahan and Mădălin Guţă

Phys. Rev. A 98, 052137 – Published 29 November 2018

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.

Received 4 September 2018

DOI:https://doi.org/10.1103/PhysRevA.98.052137

Physics Subject Headings (PhySH)

Dynamical phase transitions Open quantum systems Photon statistics Quantum fluctuations & noise Quantum master equation Quantum optics with artificial atoms

Atomic, Molecular & OpticalStatistical Physics & ThermodynamicsQuantum Information, Science & Technology

Authors & Affiliations

Juan P. Garrahan^1,2 and Mădălin Guţă^3,2

¹School of Physics and Astronomy, University of Nottingham, Nottingham NG7 2RD, United Kingdom
²Centre for the Mathematics and Theoretical Physics of Quantum Non-equilibrium Systems, University of Nottingham, Nottingham NG7 2RD, United Kingdom
³School of Mathematical Sciences, University of Nottingham, Nottingham NG7 2RD, United Kingdom

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Issue

Vol. 98, Iss. 5 — November 2018

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Images

Figure 1
(a) Dissipative three-level model. Levels 0 and 1 span the bright subspace, with level 2 the shelving state. (In Ref. [5] states 0,1,2 are called $G, B, D$ , respectively.) (b) Typical emission trajectory and sketch of the control scheme. (c) Survival probabilities $S (t)$ for the original dynamics (black dotted), for the controlled dynamics with $U_{Δ t}$ and $Δ t = 3$ (red full), and for the controlled dynamics with $U_{2}$ and $Δ t = 3 / 2$ (blue dashed); time in units of $Ω_{01}^{- 1}$ . Inset: probabilities of occupation $p_{0, 1, 2}$ of the states $| 0, 1, 2 〉$ as a function of time after the last renewal to $| 0 〉$ . The dotted and dashed lines indicate the values of $Δ t$ for the results in Fig. 2. (d) Representative emission trajectories for the two control dynamics of Sec. 4, that with $U_{Δ t}$ and $Δ t = 3$ (red) at the top, and that with $U_{2}$ and $Δ t = 1.5$ (blue) at the bottom. Parameters: $Ω_{01} = 1, Ω_{02} = 1 / 10, γ = 4$ . (All plotted quantities are in dimensionless units.)
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Figure 2
(a) LD scaled cumulant generating functions $θ (s)$ for the original dynamics (black dotted), for the controlled dynamics with $U_{Δ t}$ and $Δ t = 3$ (red full), and for the controlled dynamics with $U_{2}$ and $Δ t = 3 / 2$ (blue dashed). (b) $s$ -dependent activities (scaled number of emissions) $k (s) = - θ^{'} (s)$ for the three dynamics. (c) Activity susceptibilities (variances of $k$ scaled by time) $χ (s) = θ^{''} (s)$ for the three dynamics (the red curve divided by 3 for ease of comparison). (d) Scaled logarithm of the probability of the number of emissions in the three dynamics; abscissa shifted by $〈 k 〉$ . The gray dot-dashed curve is the corresponding Poisson distribution with the same average as the black dotted curve. Parameters: $Ω_{01} = 1, Ω_{02} = 1 / 10, γ = 4$ . (All plotted quantities are in dimensionless units.)
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Figure 3
(a) Average rate of emissions $〈 k 〉 = - θ^{'} (0)$ as a function of control time $Δ t$ , for the original dynamics (black, independent of $Δ t$ ), for the controlled dynamics with $U_{Δ t}$ (red circles), and for the controlled dynamics with $U_{2}$ (blue squares). (b) Corresponding emission susceptibilities $χ = θ^{''} (0)$ . Parameters: $Ω_{01} = 1, Ω_{02} = 1 / 10, γ = 4$ . (All plotted quantities are in dimensionless units.)
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Figure 4
Repeated control within no-jump periods. (a) LD scaled cumulant generating functions $θ (s)$ for the original dynamics (black dotted) and for the controlled dynamics $U_{Δ t}^{'}$ applied repeatedly at intervals $Δ t = 3$ within no-emission periods (magenta full). (b) $s$ -dependent activities $k (s) = - θ^{'} (s)$ for the two dynamics. Inset: activity susceptibilities $χ (s) = θ^{''} (s)$ for the three dynamics. (c) Scaled logarithm of the probability of the number of emissions in the two dynamics; abscissa shifted by $〈 k 〉$ . The gray dashed curve is the corresponding Poisson distribution with the same average as the black dotted curve. (d) Average rate of emissions $〈 k 〉 = - θ^{'} (0)$ as a function of control time $Δ t$ for the two dynamics. Inset: corresponding emission susceptibilities $χ = θ^{''} (0)$ . Parameters: $Ω_{01} = 1, Ω_{02} = 1 / 10, γ = 4$ . (All plotted quantities are in dimensionless units.)
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