ON THE QUANTUM EVOLUTION OF CHAOTIC SYSTEMS AFFECTED BY REPEATED FREQUENT MEASUREMENT
ON THE QUANTUM EVOLUTION OF CHAOTIC SYSTEMS AFFECTED BY REPEATED FREQUENT MEASUREMENT
B. Kaulakys
备注：
4 pages, LaTEX, no figures, to be published in Quantum Communication and Measurement, Ed. by V. P. Belavkin, et all. Plenum Pbl., 1995, 196-200 The article is replaced because of LaTEX bugs.
We investigate the effect of repeated measurement for quantum dynamics of the suppressed systems which classical counterparts exhibit chaos. The essential feature of such systems is the quantum localization phenomena strongly limiting motion in the energy space. Repeated frequent measurement of suppressed systems results to the delocalization. Time evolution of the observed chaotic systems becomes close to the classical frequently broken diffusion-like process described by rate equations for the probabilities rather than for amplitudes.
A method is introduced whereby two non-interacting quantum subsystems, that each interact with a third subsystem, are entangled via repeated projective measurements of the state of the third subsystem. A variety of physical examples are presented. The method can be used to establish long range entanglement between distant parties in one parallel measurement step, thus obviating the need for entanglement swapping.
Repeated observations inhibit the coherent evolution of quantum states through the quantum Zeno effect. In multi-qubit systems this effect provides new opportunities to control complex quantum states. Here, we experimentally demonstrate that repeatedly projecting joint observables of multiple spins creates coherent quantum Zeno subspaces and simultaneously suppresses dephasing caused by the environment. We encode up to two logical qubits in these subspaces and show that the enhancement of the dephasing time with increasing number of projections follows a scaling law that is independent of the …
We study entropy production (EP) in processes involving repeated quantum measurements of finite quantum systems. Adopting a dynamical system approach, we develop a thermodynamic formalism for the EP and study fine aspects of irreversibility related to the hypothesis testing of the arrow of time. Under a suitable chaoticity assumption, we establish a Large Deviation Principle and a Fluctuation Theorem for the EP.
We study the effect of frequent projective measurements on the dynamics of quantum self-sustaining systems, by considering the prototypical example of the quantum Van der Pol oscillator. Quantum fluctuations are responsible for phase diffusion which progressively blurs the semiclassical limit cycle dynamics and synchronization, either to an external driving, or between two coupled self-sustained oscillators. We show that by subjecting the system to repeated measurements of heterodyne type at an appropriate repetition frequency one can significantly suppress phase diffusion without spoiling the…
The dynamics of a kicked quantum system undergoing repeated measurements of momentum is investigated. A diffusive behavior is obtained even when the dynamics of the classical counterpart is not chaotic. The diffusion coefficient is explicitly computed for a large class of Hamiltonians and compared to the classical case.
We investigate the dynamics of a kicked particle in an infinite square well undergoing frequent measurements of energy. For a large class of periodic kicking force, constant diffusion is found in such a non-KAM system. The influence of phase shift of the kicking potential on the short-time dynamical behavior is discussed. The general asymptotical measurement-assisted diffusion rate is obtained. The entanglement between the particle and the measuring apparatus is investigated. There exist two distinct dynamical behaviors of entanglement. The bipartite entanglement grows with the kicking steps a…
The effect of entangling evolution induced by frequently repeated quantum measurement is presented. The interesting possibility of conditional freezing the system in maximally entangled state out of Zeno effect regime is also revealed. The illustration of the phenomena in terms of dynamical version of ``interaction free'' measurement is presented. Some general conclusions are provided.
Unitary designs from perturbed time evolutions of a chaotic Hamiltonian
International Center for Quantum Materials, School of Physics, Peking University（北京大学物理学院量子材料中心）；Wilczek Quantum Center, Shanghai Institute for Advanced Studies, University of Science and Technology of China（中国科学院大学上海高等研究院吴文俊亚洲数学中心）；Hefei National Laboratory（合肥国家实验室）；Beijing Key Laboratory of Quantum Devices, Peking University（北京大学量子器件北京市重点实验室）
The quantum-classical correspondence for dynamics of the nonlinear classically chaotic systems is analysed. The problem of quantum chaos consists of two parts: the quasiclassical quantisation of the chaotic systems and attempts to understand the classical chaos in terms of quantum mechanics. The first question has been partially solved by the Gutzwiller semiclassical trace formula for the eigenvalues of chaotic systems, while the classical chaos may be derived from quantum equations only introducing the decoherence process due to interaction with system's environment or intermediate frequent m…
We study the dynamics of a "kicked" quantum system undergoing repeated measurements of momentum. A diffusive behavior is obtained for a large class of Hamiltonians, even when the dynamics of the classical counterpart is not chaotic. These results can be interpreted in classical terms by making use of a "randomized" classical map. We compute the transition probability for the action variable and consider the semiclassical limit.
We demonstrate that repeated measurements in disordered systems can induce quantum anti-Zeno effect under certain condition to enhance quantum transport. The enhancement of energy transfer is really exhibited with a simple model under repeated measurements. The optimal measurement interval for the anti-Zeno effect and the maximal efficiency of energy transfer are specified in terms of the relevant physical parameters. Since the environment acts as frequent measurements on the system, the decoherence-induced energy transfer, which has been discussed recently for photosynthetic complexes, may be…
We provide a general dynamical approach for the quantum Zeno and anti-Zeno effects in an open quantum system under repeated non-demolition measurements. In our approach the repeated measurements are described by a general dynamical model without the wave function collapse postulation. Based on that model, we further study both the short-time and long-time evolutions of the open quantum system under repeated non-demolition measurements, and derive the measurement-modified decay rates of the excited state. In the cases with frequent ideal measurements at zero-temperature, we re-obtain the same d…
We study the open system dynamics of a circuit QED model operating in the ultrastrong coupling regime. If the resonator is pumped periodically in time the underlying classical system is chaotic. Indeed, the periodically driven Jaynes-Cummings model in the Born-Oppenheimer approximation resembles a Duffing oscillator which in the classical limit is a well-known example of a chaotic system. Detection of the field quadrature of the output field acts as an effective position measurement of the oscillator. We address how such detection affects the quantum chaotic evolution in this bipartite system.…
We find quantum signatures of classical chaos in various metrics of information gain in quantum tomography. We employ a quantum state estimator based on weak collective measurements of an ensemble of identically prepared systems. The tomographic measurement record consists of a sequence of expectation values of a Hermitian operator that evolves under repeated application of the Floquet map of the quantum kicked top. We find an increase in information gain and hence higher fidelities in the reconstruction algorithm when the chaoticity parameter map increases. The results are well predicted by r…
Prevention of a quantum system's time evolution by repetitive, frequent measurements of the system's state has been called the quantum Zeno effect (or paradox). Here we investigate theoretically and numerically the effect of repeated measurements on the quantum dynamics of the multilevel systems that exhibit the quantum localization of the classical chaos. The analysis is based on the wave function and Schroedinger equation, without introduction of the density matrix. We show how the quantum Zeno effect in simple few-level systems can be recovered and understood by formal modeling the measurem…
We propose to analyse the statistical properties of a sequence of vectors using the spectrum of the associated Gram matrix. Such sequences arise e.g. by the repeated action of a deterministic kicked quantum dynamics on an initial condition or by a random process. We argue that, when the number of time-steps, suitably scaled with respect to $\hbar$, increases, the limiting eigenvalue distribution of the Gram matrix reflects the possible quantum chaoticity of the original system as it tends to its classical limit. This idea is subsequently applied to study the long-time properties of sequences o…
Diagnosing chaos with projected ensembles of process tensors
Trinity College Dublin（都柏林三一学院）；Universität zu Köln（科隆大学）；Institut für Theoretische Physik, Universität zu Köln（科隆大学理论物理研究所）；Monash University（蒙纳士大学）；Singapore University of Technology and Design（新加坡科技设计大学）；King’s College London（伦敦国王学院）
Repeated measurements of a quantum particle to check its presence in a region of space was proposed long ago [G. R. Allcock, Ann. Phys. {\bf 53}, 286 (1969)] as a natural way to determine the distribution of times of arrival at the orthogonal subspace, but the method was discarded because of the quantum Zeno effect: in the limit of very frequent measurements the wave function is reflected and remains in the original subspace. We show that by normalizing the small bits of arriving (removed) norm, an ideal time distribution emerges in correspondence with a classical local-kinetic-energy distribu…
