Non-stationary Quantum States Research Articles

Nonstationary Laguerre–Gaussian states in a Magnetic Field

Abstract The Landau states of electrons with orbital angular momentum in magnetic fields are important in the quantum theories of metals and of synchrotron radiation at storage rings, in relativistic astrophysics of neutron stars, and in many other areas. In realistic scenarios, electrons are often born inside the field or injected from a field-free region, requiring nonstationary quantum states to account for boundary or initial conditions. This study presents nonstationary Laguerre–Gaussian (NSLG) states in a longitudinal magnetic field, characterizing vortex electrons after their transfer from vacuum to the field. Comparisons with Landau states and calculations of observables such as mean energy and root-mean-square (r.m.s.) radius show that the r.m.s. radius of the electron packet in the NSLG state oscillates in time around a significantly larger value than that of the Landau state. This quantum effect of oscillations is due to boundary conditions and can potentially be observed in various problems, particularly when using magnetic lenses of electron microscopes and linear accelerators. Analogies are drawn between a quantum wave packet and a classical beam of many particles in phase space, including the calculation of mean emittance of the NSLG state as a measure of its quantum nature.

Non-stationary quasi-classical states of a charged particle in a strong magnetic field under conditions of the dissipative medium

Based on the quasi-classical approximation, a general approach is proposed for constructing non-stationary quantum states of a charged particle in a magnetic field, when the dissipative forces of viscous friction and drag, proportional to the velocity and the square of the velocity, respectively, are also significant. The corresponding quasi-classical Green’s function is found, with the help of which the squeezed and coherent states of the particle are studied. It is shown that the dissipation and a magnetic field suppress the quantum properties of the particle. This is especially true for the transverse motion with respect to the magnetic field. Over time, the coherent and squeezed states transform into the same static state, which is characterized by a zero uncertainty of the transverse coordinates and an uncertainty of the longitudinal coordinate, which contains information about the initial velocity of the particle.

Density Matrix via Few Dominant Observables for the Ultrafast Non-Radiative Decay in Pyrazine.

Unraveling the density matrix of a non-stationary quantum state as an explicit function of a few observables provides a complementary view of quantum dynamics. We have recently developed a practical way to identify the minimal set of the dominant observables that govern the quantal dynamics even in the case of strong non-adiabatic effects and large anharmonicity [Komarova et al., J. Chem. Phys. 155, 204110 (2021)]. Fast convergence in the number of the dominant contributions is achieved when instead of the density matrix we describe the time-evolution of the surprisal, the logarithm of the density operator. In the present work, we illustrate the efficiency of the proposed approach using an example of the early time dynamics in pyrazine in a Hilbert space accounting for up to four vibrational normal modes, {Q10a, Q6a, Q1, and Q9a}, and two coupled electronic states, the optically dark and the bright states. Dynamics in four-dimensional (4D) configurational space involve 19,600 vibronic eigenstates. Our results reveal that the rate of the ultrafast population decay as well as the shape of the nuclear wave packets in 2D, accounting only for {Q10a,Q6a} normal modes, are accurately captured with only six dominant time-independent observables in the surprisal. Extension of the dynamics to 3D and 4D vibrational subspace requires only five additional constraints. The time-evolution of a quantum state in 4D vibrational space on two electronic states is thus compacted to only 11 time-dependent coefficients of these observables.

Efficient Semiclassical Evaluation of Electronic Coherences in Polyatomic Molecules

Exposing a molecule to intense light pulses may bring this molecule to a nonstationary quantum state, thus launching correlated dynamics of electronic and nuclear subsystems. Although much had been achieved in the understanding of fundamental physics behind the electron-nuclear interactions and dynamics, accurate numerical simulations of light-induced processes taking place in polyatomic molecules remain a formidable challenge. Here, we review a recently developed theoretical approach for evaluating electronic coherences in molecules, in which the ultrafast electronic dynamics is coupled to nuclear motion. The presented technique, which combines accurate ab initio on-the-fly simulations of electronic structure with efficient semiclassical procedure to compute the dynamics of nuclear wave packets, is not only computationally efficient, but also can help shed light on the underlying physical mechanisms of decoherence and revival of the electronic coherences driven by nuclear rearrangement.

Adaptive quantum state estimation for dynamic quantum states

We propose an adaptive quantum state estimation method for nonstationary quantum states and verify the method by numerical simulations and experimental investigations. Adaptive quantum state estimation provides an asymptotically optimal scheme for estimating an unknown input quantum state by updating the measurement configuration upon the detection of each quantum. However, previous methods are only valid for quanta with the same quantum state (a stationary state). By adopting the likelihood function for a fixed number of recent detection results, our sequential adaptive quantum state estimation allows quantum states changing in time to be estimated. The numerical simulation results and experimental demonstration using photons agree well with the theoretical predictions. This method will find applications in various fields where dynamically changing quantum states need to be estimated.

Conditional spectroscopy via nonstationary optical homodyne quantum state tomography

Continuous variable quantum state tomography is one of the most powerful techniques to study the properties of light fields in quantum optics. However, the need for a fixed phase reference has so far prevented widespread usage in other fields such as semiconductor spectroscopy. Here, we introduce non-stationary quantum state tomography, which adapts the technique to the special requirements of ultrafast spectroscopy. In detail, we gain access to the amplitude and phase of light fields with a temporal resolution of about 100\,fs without the need for a fixed phase reference. Further, we show how our technique allows us to perform conditional studies of stochastic dynamics that are inaccessible experimentally by conventional means, and demonstrate the capabilities experimentally by monitoring the stochastic dynamics of a thermal light field on the sub-ps scale. Finally, we discuss differences and similarities to more standard Hanbury Brown-Twiss photon correlation experiments, which may be considered as the discrete variable analogues of our technique.

Trojan Quantum Walks

We investigate the transport properties and entanglement between spin and position of one-dimensional quantum walks starting from a qubit over position states following a delta-like (local state) and Gaussian (delocalized state) distributions. We find out that if the initial state is delocalized enough and a NOT gate reflects this state backwards, then the interference pattern extinguishes the position dispersion without preventing the propagation of the state. This effect allows the creation of a Trojan wave packet, a non-spreading and non-stationary double-peak quantum state.

Exact time-dependent states for throat quantized toroidal AdS black holes

We investigate exact non-stationary quantum states of vacuum toroidal black holes with a negative cosmological constant in arbitrary dimensions using the framework of throat quantization pioneered by Louko and M\"akel\"a for Schwarzschild black holes. The system is equivalent to a harmonic oscillator on the half line, in which the central singularity is resolved quantum mechanically by imposing suitable boundary conditions that preserve unitarity. We identify two suitable families of exact time-dependent wave functions with Dirichlet or Neumann boundary conditions at the location of the classical singularity. We find that for highly non-stationary states of large-mass black holes, quantum fluctuations are not negligible in one family, while they are greatly suppressed in the other. The latter, therefore, may provide candidates for describing the dynamics of semi-classical black holes.

Topological origin of quantum mechanical vacuum transitions and tunneling

The quantum transition between shifted zero-mode wave functions is shown to be induced by the systematic deformation of topological and non-topological defects that support the one-dimensional double-well (DW) potential tunneling dynamics. The topological profile of the zero-mode ground state, [Formula: see text], and the first excited state, [Formula: see text], of DW potentials are obtained through the analytical technique of topological defect deformation. Deformed defects create two inequivalent topological scenarios connected by a symmetry breaking that support the quantum conversion of a zero-mode stable vacuum into an unstable tachyonic quantum state. Our theoretical findings reveal the topological origin of two-level models where a nonstationary quantum state of unitary evolution, [Formula: see text], that exhibits a stable tunneling dynamics, is converted into a quantum superposition involving a self-vanishing tachyonic mode, [Formula: see text], that parametrizes a tunneling coherent destruction. The non-classical nature of the symmetry breaking dynamics is recreated in terms of the single particle quantum mechanics of one-dimensional DW potentials.

Optical field-strength generalized polarization of non-stationary quantum states in waveguiding photonic devices

A quantum analysis of the generalized polarization properties of multimode non-stationary states based on their optical field-strength probability distributions is presented. The quantum generalized polarization is understood as a significant confinement of the probability distribution along certain regions of a multidimensional optical field-strength space. The analysis is addressed to quantum states generated in multimode linear and nonlinear waveguiding (integrated) photonic devices, such as multimode waveguiding directional couplers and waveguiding parametric amplifiers, whose modes fulfill a spatial modal orthogonality. In particular, the generalized polarization degree of coherent, squeezed and Schrödinger’s cat states is analyzed.

Quantum description of a time-dependent mesoscopic RLC circuit

In this paper, we present a comprehensive quantum description of a mesoscopic RLC circuit with time-dependent resistance, inductance and capacitance. Based on the dynamical invariant method and using quadratic invariants, we derive exact nonstationary quantum states for this circuit and write them in terms of solutions of the Milne–Pinney equation. Afterwards, we use quadratic invariants to construct coherent states for this quantized system and employ them to investigate quantum properties of the RLC circuit. In particular, we show that the product of the quantum fluctuations of the charge and the magnetic flux does not satisfy the minimum uncertainty relation.

Quasi-coherent states for a photon in time varying dielectric media

In this study, we derive the quasi-coherent states for a photon in a medium with time varying dielectric permittivity ϵ0eηt. We introduce a new kind of holomorphic coordinates and solve the Schrödinger equation for a harmonic oscillator with the time dependent parameters by reducing it to the Riccati equation for which the nonstationary solution gives the squeezed states of a photon with non-minimum uncertainties. We also derive the quasi-coherent states and discrete, nonstationary quantum states in the configuration space of a photon.

Rydberg wave packets in molecules

Rydberg wave packets are important non-stationary quantum states, bordering on the classical limit of high principal quantum numbers. Molecular Rydberg wave packets are much more complicated than their well-studied atomic counterparts and exhibit many of the dynamical complications shown by larger, more chemical, systems. The interplay between molecular and electronic phase has important implications in coherent control strategies. This review describes both the theory behind molecular Rydberg wave packets and the experimental detail required to observe their dynamics, and is illustrated with examples from both experiment and theory.

Complete reconstruction of the quantum state of a single-photon wave packet absorbed by a Doppler-broadened transition.

An idea for how to reconstruct the quantum state of a nonstationary single-photon wave packet absorbed in a macroscopic medium with inhomogeneously broadened lines is presented. An analytical treatment of the problem is performed and the requirements on the proposed scheme for complete recovery of the recorded nonstationary quantum state with a probability close to unity is described. The physical nature of the present scheme is also discussed.

Relativistic quantum protocols: Bit commitment and coin tossing

New relativistic quantum protocols realizing the bit commitment and coin tossing schemes are proposed. The protocols are based on the idea that spatially extended nonstationary orthogonal quantum states inaccessible for measurement cannot be unambiguously distinguished. As the states are transmitted from the region controlled by one party to the region accessible for measurement by the other party, the states become reliably distinguishable when accessed as a whole. Essential points of the protocol are both the quantum character of states and the existence of an ultimate signal propagation speed dictated by special relativity.

Bohm's Mysterious 'Quantum Force' and 'Active Information': Alternative Interpretation and Statistical Properties

Abstract An alternative interpretation to Bohm’s ‘quantum force’ and ‘active information’ is proposed. Numerical evidence is presented, which suggests that the time series of Bohm’s ‘quantum force’ evaluated at the Bohmian position for non-stationary quantum states are typically non-Gaussian stable distributed with a flat power spectrum in classically chaotic Hamitonian systems. An important implication of these statistical properties is briefly mentioned

Controlled quantum evolutions and transitions

We study the nonstationary solutions of Fokker-Planck equations associated to either stationary or nonstationary quantum states. In particular we discuss the stationary states of quantum systems with singular velocity fields. We introduce a technique that allows to realize arbitrary evolutions ruled by these equations, to account for controlled quantum transitions. The method is illustrated by presenting the detailed treatment of the transition probabilities and of the controlling time-dependent potentials associated to the transitions between the stationary, the coherent, and the squeezed states of the harmonic oscillator. Possible extensions to anharmonic systems and mixed states are briefly discussed and assessed.

Scaling laws and correlation lengths of quantum and classical ergodic states

The semiclassical analog of the spatial quantum wavefunction correlation is shown to be identical, over short ranges, to its quantum counterpart for the vast majority of high-lying stadium eigenstates. Also, the semiclassical and pure quantum correlation lengths are shown to scale as the local de Bfoglie wavelength, a feature related to quantum ergodicity. Cross correlation and the time evolution of correlation lengths for non-stationary quantum states are then examined and the latter is shown to be a near constant of the motion for chaotic wavepackets. This characteristic may relate to features of quantum mixing.

On the relaxation of an N-level system under gauss noise

In the evolution of an N-level system interacting with an external noise there is in general a specific phase transition from damped oscillations to an aperiodic motion when the intensity of the external noise increases. But in some cases the region of aperiodic motion can be absent. On the other hand, several such regions can exist. Under some conditions a strong interaction with environment can stabilize a nonstationary quantum state of the system.

Classical methods in molecular scattering: a continuous quantization procedure

A simple improvement of the quasiclassical histogram approximation in molecular scattering is presented, based on a continuity ansatz that relates arbitrary classical actions and non-stationary quantum states. This procedure is applied to the case of collinear collisions in atom—harmonic oscillator systems and increases the accuracy of standard quasiclassical methods