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We study a dissipative quantum mechanical model of the projective measurement of a qubit. We demonstrate how a correspondence limit, damped quantum oscillator can realise chaotic-like or periodic trajectories that emerge in sympathy with the projection of the qubit state, providing a model of the measurement process.
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The prediction of the response of a closed system to external perturbations is one of the central problems in quantum mechanics, and in this respect, the local density of states (LDOS) provides an in- depth description of such a response. The LDOS is the distribution of the overlaps squared connecting the set of eigenfunctions with the perturbed one. Here, we show that in the case of closed systems with classically chaotic dynamics, the LDOS is a Breit-Wigner distribution under very general perturbations of arbitrary high intensity. Consequently, we derive a semiclassical expression for the width of the LDOS which is shown to be very accurate for paradigmatic systems of quantum chaos. This Letter demonstrates the universal response of quantum systems with classically chaotic dynamics.
The second order photon correlation g^(2)(tau) of a chaotic optical-feedback semiconductor laser is precisely measured using a Hanbury Brown-Twiss interferometer. The accurate g^(2)(tau) with non-zero delay time is obtained experimentally from the photon pair time interval distribution through a ninth-order self-convolution correction. The experimental results agree well with the theoretical analysis. The relative error of g^(2)(tau) is no more than 0.005 within 50 ns delay time. The bunching effect and coherence time of the chaotic laser are measured via the precise photon correlation technique. This technique provides a new tool to improve the accuracy of g^(2)(tau) measurement and boost applications of quantum statistics and correlation.
Time-delay signature (TDS) suppression of semiconductor lasers with external optical feedback is necessary to ensure the security of chaos-based secure communications. Here we numerically and experimentally demonstrate a technique to effectively suppress the TDS of chaotic lasers using quantum noise. The TDS and dynamical complexity are quantified using the autocorrelation function and normalized permutation entropy at the feedback delay time, respectively. Quantum noise from quadrature fluctuations of vacuum state is prepared through balanced homodyne measurement. The effects of strength and bandwidth of quantum noise on chaotic TDS suppression and complexity enhancement are investigated numerically and experimentally. Compared to the original dynamics, the TDS of this quantum-noise improved chaos is suppressed up to 94% and the bandwidth suppression ratio of quantum noise to chaotic laser is 1:25. The experiment agrees well with the theory. The improved chaotic laser is potentially beneficial to chaos-based random number generation and secure communication.
We study the quantum to classical transition in a chaotic system surrounded by a diffusive environment. The emergence of classicality is monitored by the Renyi entropy, a measure of the entanglement of a system with its environment. We show that the Renyi entropy has a transition from quantum to classical behavior that scales with $hbar^2_{rm eff}/D$, where $hbar_{rm eff}$ is the effective Planck constant and $D$ is the strength of the noise. However, it was recently shown that a different scaling law controls the quantum to classical transition when it is measured comparing the corresponding phase space distributions. We discuss here the meaning of both scalings in the precise definition of a frontier between the classical and quantum behavior. We also show that there are quantum coherences that the Renyi entropy is unable to detect which questions its use in the studies of decoherence.
When applied to dynamical systems, both classical and quantum, time periodic modulations can produce complex non-equilibrium states which are often termed chaotic`. Being well understood within the unitary Hamiltonian framework, this phenomenon is less explored in open quantum systems. Here we consider quantum chaotic state emerging in a leaky cavity, when an intracavity photonic mode is coherently pumped with the intensity varying periodically in time. We show that a single spin, when placed inside the cavity and coupled to the mode, can moderate transitions between regular and chaotic regimes -- that are identified by using quantum Lyapunov exponents -- and thus can be used to control the degree of chaos. In an experiment, these transitions can be detected by analyzing photon emission statistics.
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