Real-time quantum trajectories for classically allowed dynamics in strong laser fields (original) (raw)
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Dynamical Localization: Classical vs Quantum Oscillations in Momentum Spread of Cold Atoms
Physical Review Letters, 1995
We investigate the classical and quantum dynamics of atoms moving in a phase-modulated standing light field. In both cases the width of the momentum distribution exhibits characteristic oscillations as a function of the modulation amplitude. We argue that at the maxima of these oscillations the system is chaotic, whereas in the valleys it is almost regular. Quantum localization appears only in the chaotic regime. We connect our analysis with a recent experiment [F. Moore et al., Phys. Rev. Lett. 73, 2974]. PACS numbers: 05.45.+b, 42.50.Lc, 42.50.Vk Most recently the description of cold atoms [1] in the framework of atom optics [2] has opened [3-5] a new avenue in the search for fingerprints of classical chaos in quantum systems: A strongly detuned atom in a standing light field moves like a particle in a spatially periodic potential . An atom in a phase-modulated light field additionally experiences a time dependent force . Classically, the resulting motion can be chaotic . But how does classical chaos manifest itself in the quantum dynamics of the atom and how to reach the quantum domain? The landmark experiment by the Austin group answers these questions: The measured momentum transfer of atoms in a phase-modulated light field shows the characteristic signature of quantum chaos: dynamical localization. Moreover, the appropriate choice of the experimental parameters such as the wave number of the standing light field or the modulation frequency allows one to step from regimes which ask for a classical description to regimes which ask for a quantum description.
The Journal of Physical Chemistry A, 2012
The dynamics of molecules under strong laser pulses is characterized by large Stark effects that modify and reshape the electronic potentials, known as laser-induced potentials (LIPs). If the time scale of the interaction is slow enough that the nuclear positions can adapt to these externally driven changes, the dynamics proceeds by adiabatic following, where the nuclei gain very little kinetic energy during the process. In this regime we show that the molecular dynamics can be simulated quite accurately by a semiclassical surfacehopping scheme formulated in the adiabatic representation. The nuclear motion is then influenced by the gradients of the laser-modified potentials, and nonadiabatic couplings are seen as transitions between the LIPs. As an example, we simulate the process of adiabatic passage by light induced potentials in Na 2 using the surfacehopping technique both in the diabatic representation based on molecular potentials and in the adiabatic representation based on LIPs, showing how the choice of the representation is crucial in reproducing the results obtained by exact quantum dynamical calculations.
Continuous Transitions Between Quantum and Classical Motions
arXiv (Cornell University), 2016
Using a nonlinear Schrödinger equation for the wave function of all systems, continuous transitions between quantum and classical motions are demonstrated for (i) the double-slit set up, (ii) the 2D harmonic oscillator and (iii) the hydrogen-like atom, all of which are of empirical interest.
Atomic motion in laser light: connection between semiclassical and quantum descriptions
Journal of Physics B: Atomic and Molecular Physics
The quantum kinetic equation describing slow atomic motion in laser light is derived by an operatorial method which provides mathematical expressions with a transparent physical structure. We prove in a general way that the coefficients appearing in this equation, which is of a Fokker-Planck type, are simply related to the mean value and to the correlation functions of the Heisenberg radiative force of the semiclassical approach, where the atomic position is treated classically. We derive in particular a new theoretical expression for the damping force responsible for radiative cooling'and we interpret it in terms of linear response theory. We also obtain a new crossed r-p derivative term, which does not appear in semiclassical treatments, but which we find to be very small in most situations. Finally, al1 the theoretical expressions derived in this paper are valid for any J, to Je transition and are not restricted to two-level atoms.
Dynamic versus hydrodynamic quantum trajectories
arXiv preprint arXiv:1207.0130, 2012
The behavior of classical monochromatic waves in stationary media is shown to be ruled by a novel, frequency-dependent function which we call Wave Potential, and which we show to be encoded in the structure of the Helmholtz equation. An exact, Hamiltonian, ray-based kinematical treatment, reducing to the usual eikonal approximation in the absence of Wave Potential, shows that its presence induces a mutual, perpendicular ray-coupling, which is the one and only cause of wave-like phenomena such as diffraction and interference. The Wave Potential, whose discovery does already constitute a striking novelty in the case of classical waves, turns out to play an even more important role in the quantum case. Recalling, indeed, that the time-independent Schrödinger equation (associating the motion of mono-energetic particles with stationary monochromatic matter waves) is itself a Helmholtz-like equation, the exact, ray-based treatment developed in the classical case is extended -without resorting to statistical concepts -to the exact, trajectorybased Hamiltonian dynamics of mono-energetic point-like particles. Exact, classical-looking particle trajectories may be defined, contrary to common belief, and turn out to be perpendicularly coupled by an exact, energy-dependent Wave Potential, similar in the form, but not in the physical meaning, to the statistical, energy-independent "Quantum Potential" of Bohm's theory, which is affected, as is well known, by the practical necessity of representing particles by means of statistical wave packets, moving along probability flux lines. This result, together with the connection shown to exist between Wave Potential and Uncertainty Principle, allows a novel, non-probabilistic interpretation of Wave Mechanics.
An introduction to the problem of bridging quantum and classical dynamics
The European Physical Journal Special Topics, 2015
Simulating the exact quantum dynamics of realistic interacting systems is presently a task beyond reach but for the smallest of them, as the numerical cost for solving the time-dependent Schrödinger equation scales exponentially with the number of degrees of freedom. Mixed quantum-classical methods attempt to solve this problem by starting from a full quantum description of the system and subsequently partitioning the degrees of freedom in two subsets: the quantum subsystem and the bath. A classical limit is then taken for the bath while preserving, at least approximately, the quantum evolution of the subsystem. A key, as yet not fully resolved, theoretical question is how to do so by constructing a consistent description of the overall dynamics. An exhaustive review of this class of methods is beyond the scope of this paper and we shall limit ourselves to present, as an example, a specific approach, known as the LANDM-Map method. The method stems from an attempt at taking a rigorous limit for the classical degrees of freedom starting from a path integral formulation of the full quantum problem. The results that we discuss are not new, but our intent here is to present them as an introduction to the problem of mixed quantum classical dynamics. We shall also indicate a broad classification of the available approaches, their limitations, and some open questions in this field.
Equivalence principle: tunnelling, quantized spectra and trajectories from the quantum HJ equation
Physics Letters B, 1999
A basic aspect of the recently proposed approach to quantum mechanics is that no use of any axiomatic interpretation of the wave function is made. In particular, the quantum potential turns out to be an intrinsic potential energy of the particle, which, similarly to the relativistic rest energy, is never vanishing. This is related to the tunnel effect, a consequence of the fact that the conjugate momentum field is real even in the classically forbidden regions.