Stable macroscopic quantum superpositions

We study the stability of superpositions of macroscopically distinct quantum states under decoherence. We introduce a class of quantum states with entanglement features similar to Greenberger-Horne-Zeilinger (GHZ) states, but with an inherent stability against noise and decoherence. We show that in contrast to GHZ states, these so-called concatenated GHZ states remain multipartite entangled even for macroscopic numbers of particles and can be used for quantum metrology in noisy environments. We also propose a scalable experimental realization of these states using existing ion-trap setups.     

Temperature can enhance coherent oscillations at a Landau-Zener transition

We consider sweeping a system through a Landau-Zener avoided crossing, when that system is also coupled to an environment or noise. Unsurprisingly, we find that decoherence suppresses the coherent oscillations of quantum superpositions of system states, as superpositions decohere into mixed states. However, we also find an effect we call "Lamb-assisted coherent oscillations," in which a Lamb shift exponentially enhances the coherent-oscillation amplitude. This dominates for high-frequency environments such as super-Ohmic environments, where the coherent oscillations can grow exponentially as either the environment coupling or temperature are increased. The effect could be used as an experimental probe for high-frequency environments in such systems as molecular magnets, solid-state qubits, spin-polarized gases (neutrons or He3), or Bose condensates.     

Decoherence in a system of many two-level atoms

I show that the decoherence in a system of degenerate two-level atoms interacting with a bosonic heat bath is for any number of atoms governed by a generalized Hamming distance (called "decoherence metric") between the superposed quantum states, with a time-dependent metric tensor that is specific for the heat bath. The decoherence metric allows for the complete characterization of the decoherence of all possible superpositions of many-particle states, and can be applied to minimize the overall decoherence in a quantum memory. For qubits which are far apart, the decoherence is given by a function describing single-qubit decoherence times the standard Hamming distance. I apply the theory to cold atoms in an optical lattice interacting with blackbody radiation.     

Wigner distribution,nonclassicality and decoherence of generalized and reciprocal binomial states

There are quantum states of light that can be expressed as finite superpositions of Fock states (FSFS). We demonstrate the nonclassicality of an arbitrary FSFS by means of its phase space distributions such as the Wigner function and the Q-function. The decoherence of the FSFS is studied by considering the time evolution of its Wigner function in amplitude decay and phase damping channels. As examples, we determine the nonclassicality and decoherence of generalized and reciprocal binomial states.     

On the role of entanglement in Schrödinger’s cat paradox

In this paper we re-investigate the core of Schrödinger’s “cat paradox”. We argue that one has to distinguish clearly between superpositions of macroscopic cat states |?〉 + |?〉 and superpositions of entangled states |?, ↑〉 + |?, ↓〉 which comprise both the state of the cat (?=alive, ?=dead) and the radioactive substance (↑=not decayed, ↓=decayed). It is shown, that in the case of the cat experiment recourse to decoherence or other mechanisms is not necessary in order to explain the absence of macroscopic superpositions. Additionally, we present modified versions of two quantum optical experiments as experimenta crucis. Applied rigorously, quantum mechanical formalism reduces the problem to a mere pseudo-paradox.     

Mesoscopic superpositions of vibronic collective states of N trapped ions

We propose a scalable procedure to generate superpositions of motional coherent states and also entangled vibronic states in N trapped ions. Beyond their fundamental importance, these states may be of interest for quantum information processing and may be used in experimental studies on decoherence.     

Effect of one-, two-, and three-body atom loss processes on superpositions of phase states in Bose-Josephson junctions

In a two-mode Bose-Josephson junction formed by a binary mixture of ultracold atoms, macroscopic superpositions of phase states are produced during the time evolution after a sudden quench to zero of the coupling amplitude. Using quantum trajectories and an exact diagonalization of the master equation, we study the effect of one-, two-, and three-body atom losses on the superpositions by analyzing separately the amount of quantum correlations in each subspace with fixed atom number. The quantum correlations useful for atom interferometry are estimated using the quantum Fisher information. We identify the choice of parameters leading to the largest Fisher information, thereby showing that, for all kinds of loss processes, quantum correlations can be partially protected from decoherence when the losses are strongly asymmetric in the two modes.     

NMR-like control of a quantum bit superconducting circuit

Coherent superpositions of quantum states have already been demonstrated in different superconducting circuits based on Josephson junctions. These circuits are now considered for implementing quantum bits. We report on experiments in which the state of a qubit circuit, the quantronium, is efficiently manipulated using methods inspired from nuclear magnetic resonance (NMR): multipulse sequences are used to perform arbitrary operations, to improve their accuracy, and to fight decoherence.     

A stepwise planned approach to the solution of Hilbert’s sixth problem. III: Measurements and von Neumann projection/collapse rule

Supmech, the universal mechanics developed in the previous two papers (Dass, arXiv: 0909.4606[math-ph]; 1002:2061[math-ph]), accommodates both quantum and classical mechanics as subdisciplines (a brief outline is included for completeness); this feature facilitates, in a supmech-based treatment of quantum measurements, an unambiguous treatment of the apparatus as a quantum system approximated well by a classical one. Taking explicitly into consideration the fact that observations on the apparatus are made when it has ‘settled down after the measurement interaction’ and are restricted to macroscopically distinguishable pointer readings, the unwanted superpositions of (system + apparatus) states are shown to be suppressed; this provides a genuinely physics-based justification for the (traditionally postulated) von Neumann projection/collapse rule. The decoherence mechanism brought into play by the stated observational constraints is free from the objections against the traditional decoherence program.     

Change of decoherence scenario and appearance of localization due to reservoir anharmonicity

Although coupling to a super-Ohmic bosonic reservoir leads only to partial dephasing on short time scales, exponential decay of coherence appears in the Markovian limit (for long times) if anharmonicity of the reservoir is taken into account. This effect not only qualitatively changes the decoherence scenario but also leads to localization processes in which superpositions of spatially separated states dephase with a rate that depends on the distance between the localized states. As an example of the latter process, we study the decay of coherence of an electron state delocalized over two semiconductor quantum dots due to anharmonicity of phonon modes.     

A proposal to test Bell’s inequalities with mesoscopic non-local states in cavity QED

We propose a cavity quantum electrodynamics (CQED) experiment to test the violation of a Bell-type inequality using non-local mesoscopic states (NLMS). These states involve coherent field superpositions stored in two spatially-separated high-Q cavities. The inequality is expressed in terms of the measured Wigner function of the entangled two-field-mode system at four points in phase space, as proposed in [Banaszek and Wódkiewicz, Phys. Rev. Lett. 82, 2009 (1999)]. We examine the production of these entangled NLMS and the measurement of their Wigner function. The experiment involves circular Rydberg atoms and superconducting millimeter-wave cavities. We present a detailed numerical study of the optimal inequality violation and of the effect of decoherence. We discuss the range of experimental parameters making it possible to observe a locality violation and show that they correspond to realistic, albeit demanding, conditions.     

Stabilization of nonclassical states of the radiation field in a cavity by reservoir engineering

We propose an engineered reservoir inducing the relaxation of a cavity field towards nonclassical states. It is made up of two-level atoms crossing the cavity one at a time. Each atom-cavity interaction is first dispersive, then resonant, then dispersive again. The reservoir pointer states are those produced by an effective Kerr Hamiltonian acting on a coherent field. We thereby stabilize squeezed states and quantum superpositions of multiple coherent components in a cavity having a finite damping time. This robust decoherence protection method could be implemented in state-of-the-art experiments.     

Quantum speed limits for Bell-diagonal states

The lower bounds of the evolution time between two distinguishable states of a system, defined as quantum speed limit time, can characterize the maximal speed of quantum computers and communication channels. We study the quantum speed limit time between the composite quantum states and their target states in the presence of nondissipative decoherence.For the initial states with maximally mixed marginals, we obtain the exact expressions of the quantum speed limit time which mainly depend on the parameters of the initial states and the decoherence channels. Furthermore, by calculating the quantum speed limit time for the time-dependent states started from a class of initial states, we discover that the quantum speed limit time gradually decreases in time, and the decay rate of the quantum speed limit time would show a sudden change at a certain critical time. Interestingly, at the same critical time, the composite system dynamics would exhibit a sudden transition from classical decoherence to quantum decoherence.     

Coherence stability in three-level systems

We study the decoherence rate for estimating the time at which the coherence instability of a quantum pure state is onset. We analyze the coherence stability of pure states of a three-level quantum system under the effect of a bosonic reservoir and driven by two Raman classical fields. By assuming the boson systems to be in thermal states we find for a symmetric V-system a set of three states free from decoherence and, for a symmetric cascade-system, a two-dimensional subspace whose states are stable against the considered decoherence mechanism.     

Consistent Histories in Quantum Cosmology

We illustrate the crucial role played by decoherence (consistency of quantum histories) in extracting consistent quantum probabilities for alternative histories in quantum cosmology. Specifically, within a Wheeler-DeWitt quantization of a flat Friedmann-Robertson-Walker cosmological model sourced with a free massless scalar field, we calculate the probability that the universe is singular in the sense that it assumes zero volume. Classical solutions of this model are a disjoint set of expanding and contracting singular branches. A naive assessment of the behavior of quantum states which are superpositions of expanding and contracting universes suggests that a “quantum bounce” is possible i.e. that the wave function of the universe may remain peaked on a non-singular classical solution throughout its history. However, a more careful consistent histories analysis shows that for arbitrary states in the physical Hilbert space the probability of this Wheeler-DeWitt quantum universe encountering the big bang/crunch singularity is equal to unity. A quantum Wheeler-DeWitt universe is inevitably singular, and a “quantum bounce” is thus not possible in these models.     

噪声对一种三粒子量子探针态的影响

量子度量学是研究量子测量与统计推断的一门学科,主要利用量子手段来提高参数估计的精度,在量子信息处理与测量中起到关键作用.量子参数估计的一般过程包含四个步骤:探针态的制备、参数化过程、对参数化后的输出态进行测量以及根据测量结果估计待测参数.其中探针态的选取对测量精度起着至关重要的作用.然而在实际的量子探针态的制备过程中,初始探针态会受到环境噪声的影响.目前人们已经研究了W态与Greenberger-Horne-Zeilinger(GHZ)态的量子Fisher信息(QFI)在典型噪声通道下的变化行为.由于W态与GHZ态有着不同的纠缠性质,对于W态与GHZ态的叠加态的QFI动力学研究具有重要的实际意义.故此,本文主要研究典型噪声通道对这两种状态的叠加态的QFI动力学行为的影响,得出了QFI随噪声参数的变化行为.结果表明,叠加态中W态组分可明显对抗相位阻尼噪声对探针态的QFI的影响,而其中的GHZ态组分可明显对抗振幅阻尼噪声的影响,从而为在实际环境中选取高精度的参数估计过程提供参考.     

Measurement of energy eigenstates by a slow detector

We propose a method for a weak continuous measurement of the energy eigenstates of a fast quantum system by means of a slow detector. Such a detector is sensitive only to slowly changing variables, e.g., energy, while its backaction can be limited solely to decoherence of the eigenstate superpositions. We apply this scheme to the problem of detection of quantum jumps between energy eigenstates in a harmonic oscillator.     

Towards an experimental test of gravity-induced quantum state reduction

Modern developments in condensed matter and cold atom physics have made the realization of macroscopic quantum states in the laboratory everyday practice. The ready availability of these states suggests the possibility of experimentally investigating different proposals for the mechanism of quantum state reduction. One such proposal is the hypothesis of Penrose and Diósi, according to which quantum state reduction is a manifestation of the incompatibilty of general relativity and the unitary time evolution of quantum physics. Dimensional analysis suggests that Schrödinger cat type states should collapse on measurable time-scales when masses and lengths of the order of bacterial scales are involved. We analyse this hypothesis in the context of the modern experimental realizations of macroscopic quantum states. First we consider ‘micromechanical’ quantum states, analysing the capacity of an atomic force microscopy based single spin detector to measure the gravitational state reduction, but we conclude that it seems impossible to suppress environmental decoherence to the required degree. We subsequently discuss ‘split’ cold atom condensates to find out that these are at present lacking the required mass-scale by many orders of magnitude. We then extend Penrose's analysis to superpositions of mass current carrying states, and we apply this to the flux quantum bits realized in superconducting circuits. We find that the flux qubits approach the scale where gravitational state reduction should become measurable, but bridging the few remaining orders of magnitude appears to be very difficult with present day technology.     

Towards quantum superpositions of a mirror

We propose an experiment for creating quantum superposition states involving of the order of 10(14) atoms via the interaction of a single photon with a tiny mirror. This mirror, mounted on a high-quality mechanical oscillator, is part of a high-finesse optical cavity which forms one arm of a Michelson interferometer. By observing the interference of the photon only, one can study the creation and decoherence of superpositions involving the mirror. A detailed analysis of the requirements shows that the experiment is within reach using a combination of state-of-the-art technologies.