Monte Carlo Wave Function Research Articles

Optical shielding of cold collisions in blue-detuned near-resonant optical lattices

We report Monte Carlo wave-function simulation results for two colliding atoms in a blue-detuned near-resonant $J=\stackrel{\ensuremath{\rightarrow}}{1}J=1$ optical lattice. Our results show that complete optical shielding of collisions can be achieved within the lattice with suitably selected and realistic laser field parameters. More importantly, our results demonstrate that the shielding effect does not interfere with the actual trapping and cooling process, and it is produced by the lattice lasers themselves, without the need to use additional laser beams.

Quantum jump dynamics in cavity QED

We study the stochastic dynamics of the electromagnetic field in a lossless cavity interacting with a beam of two-level atoms, given that the atomic states are measured after they have crossed the cavity. The atoms first interact at the exit of the cavity with a classical laser field ℰ and then enter into a detector which measures their states. Each measurement disentangles the field and the atoms and changes in a random way the state |ψ(t)〉 of the cavity field. For weak atom-field coupling, the evolution of |ψ(t)〉 when many atoms cross the cavity and the detector is characterized by a succession of quantum jumps occurring at random times, separated by quasi-Hamiltonian evolutions, both of which depend on the laser field ℰ. For ℰ=0, the dynamics is the same as in the Monte Carlo wave function model of Dalibard et al. [Phys. Rev. Lett. 68, 580 (1992)] and Carmichael, An Open System Approach to Quantum Optics, Lecture Notes in Physics Vol. 18 (Springer, Berlin, 1991)]. The density matrix of the quantum field, obtained by averaging the projector |ψ(t)〉〈ψ(t)| over all results of the measurements, is independent of ℰ and follows the master equation of the damped harmonic oscillator at finite temperature. We provide numerical evidence showing that for large ℰ, an arbitrary initial field state |ψ(0)〉 evolves under the monitoring of the atoms and the measurements toward squeezed states |α,re2iφ〉, moving in the α-complex plane but with almost constant squeezing parameters r and φ. The values of r and φ are determined analytically. On the other hand, for ℰ=0, the dynamics transforms the initial state into Fock states |n〉 with fluctuating numbers of photons n, as shown in Kist et al. [J. Opt. B: Quantum Semiclassical Opt. 1, 251 (1999)]. In the last part, we derive the quantum jump dynamics from the linear quantum jump model proposed in Spehner and Bellissard [J. Stat. Phys. 104, 525 (2001)], for arbitrary open quantum systems having a Lindblad-type evolution. A careful derivation of the infinite jump rates limit, where the dynamics can be approximated by a diffusion process of the quantum state, is also presented.

Observation of single molecule transport at surfaces via scanning microscopies: Monte Carlo wave function study of a model problem.

We discuss experiments where the trajectories of individual molecules or atoms at surfaces are observed by means of scanning microscopy. A scanning probe moves along the surface and excites the molecule so that the molecule's location is deduced from the times at which fluorescence photons are emitted. Operation of other types of scanning microscopes can be described by similar models. The observed trajectories are inherently affected by the interaction between the molecule and the probe such that the measured diffusion coefficient depends on the frequency at which the surface is scanned. The number of photons emitted by the molecule during a scan is affected in a nontrivial way by its mobility. If photoexcitation increases the mobility, we find emission to be suppressed.

Weak transitions inA=6and 7 nuclei

The ${}^{6}\mathrm{He}$ $\ensuremath{\beta}$ decay and ${}^{7}\mathrm{Be}$ electron capture processes are studied using variational Monte Carlo wave functions, derived from a realistic Hamiltonian consisting of the Argonne ${v}_{18}$ two-nucleon and Urbana-IX three-nucleon interactions. The model for the nuclear weak axial current includes one- and two-body operators with the strength of the leading two-body term---associated with $\ensuremath{\Delta}$-isobar excitation of the nucleon---adjusted to reproduce the Gamow-Teller matrix element in tritium $\ensuremath{\beta}$ decay. The measured half-life of ${}^{6}\mathrm{He}$ is underpredicted by theory by $\ensuremath{\simeq}8%,$ while that of ${}^{7}\mathrm{Be}$ for decay into the ground and first excited states of ${}^{7}\mathrm{Li}$ is overpredicted by $\ensuremath{\simeq}9%.$ However, the experimentally known branching ratio for these latter processes is in good agreement with the calculated value. Two-body axial current contributions lead to a $\ensuremath{\simeq}1.7%$ (4.4%) increase in the value of the Gamow-Teller matrix element of ${}^{6}\mathrm{He}$ ${(}^{7}\mathrm{Be}),$ obtained with one-body currents only, and slightly worsen (appreciably improve) the agreement between the calculated and measured half-life. Corrections due to retardation effects associated with the finite lepton momentum transfers involved in the decays, as well as contributions of suppressed transitions induced by the weak vector charge and axial current operators, have also been calculated and found to be negligible.

Coherently driven and coherently pumped micromaser

We investigate the dynamics of a micromaser continuously driven by a resonant coherent field and pumped by atoms injected in superposition states. We formulate a master equation for the system, and by a Monte Carlo wave-function approach we describe the steady-state behavior as a function of atomic-transit time or driving-field intensity. The combined action of polarized atoms and driving field can lead to enhancement or suppression of coherence in system dynamics, including nonclassical effects such as quadrature squeezing, sub-Poissonian photon statistics, and revival of Rabi oscillations, as well as to shifts of the induced cavity-field phase. These results show the possibility of manipulating both the photon number and the phase of the cavity field.

Quantum diffusion of H/Ni(111) through a Monte Carlo wave function formalism.

We consider a quantum system coupled to a dissipative background with many degrees of freedom using the Monte Carlo wave function method. Instead of dealing with a density matrix which can be very highly dimensional, the method consists of integrating a stochastic Schrödinger equation with a non-Hermitian damping term in the evolution operator, and with random quantum jumps. The method is applied to the diffusion of hydrogen on the Ni(111) surface below 100 K. We show that the recent experimental diffusion data for this system can be understood through an interband activation process, followed by quantum tunneling.

Radiativeα-capture cross sections from realistic nucleon-nucleon interactions and variational Monte Carlo wave functions

We report the first calculations of cross sections for the radiative capture reactions ${}^{3}\mathrm{H}(\ensuremath{\alpha},\ensuremath{\gamma}{)}^{7}\mathrm{Li}$ and ${}^{3}\mathrm{He}(\ensuremath{\alpha},\ensuremath{\gamma}{)}^{7}\mathrm{Be}$ below 2 MeV that use wave functions derived from realistic nucleon-nucleon interactions by the variational Monte Carlo technique. After examining several small corrections to the dominant $E1$ operator, we find energy dependences for the low-energy S factors that agree reasonably with experimental measurements. There is no contradiction with the previous theoretical understanding of these processes, but the zero-energy derivative of the ${}^{3}\mathrm{H}(\ensuremath{\alpha},\ensuremath{\gamma}{)}^{7}\mathrm{Li}$ S factor is smaller than that in most models. While this method can, in principle, predict cross section normalizations, the normalizations of our results are mostly too low.

Coherently Driven Micromaser Pumped by Atoms in Superposition States

Abstract By a Monte Carlo wave function approach we describe the dynamics of a coherently driven micromaser pumped by coherently prepared atoms. The system can exhibit nonclassical effects such as quadrature squeezing, sub-Poissonian photonstatistics, and Rabi oscillations revival. The interplay between driving field and polarised atoms allows manipulating both the photon number and the phase of the cavity field. By varying either the atomic transit time or the injected field intensity, the coherence of the system dynamics can be enhanced or even suppressed, whereas the induced cavity field phase can be shifted.

Quantum master equation, Lindblad-type of dissipation and temperature dependent Monte Carlo wave-function propagation

So-called quantum-trajectory techniques have been introduced to reveal single-quantum system dynamics contained in the average ensemble description. Main application could be addressed to quantum optics of single atoms where one usually starts with the Lindblad-type of density matrix equations. Here, emphasis is put on the dissipative dynamics of molecular systems. The derivation of a temperature-dependent quantum-trajectory technique is presented starting from the widely used quantum master equation (QME) for the reduced density operator. Different applications of the resulting Monte Carlo wavefunction (MCWF) method being valid for molecular systems are given.

Tunnelling and the Born-Oppenheimer approximation in optical lattices

We study periodic well-to-well flopping of rubidium atoms in one-dimensional grey optical lattices using a nondestructive, real-time measurement technique and quantum Monte Carlo wavefunction simulations. The observed flopping rates as well as flopping rates extracted from exact band structure calculations can largely be reproduced using adiabatic models that employ the Born-Oppenheimer approximation. The adiabatic model is greatly improved by taking into account a gauge potential that is added to the usual adiabatic light-shift potential. The validity of the adiabatic model allows us to interpret the observed flopping phenomenon as periodic well-to-well tunnelling. At low intensities and in related far-off-resonant optical lattices the adiabatic model fails. There, a weak-coupling model becomes valid, which describes the well-to-well flopping as a Rabi oscillation between weakly coupled states, but not as a tunnel effect.

Dynamics of a coherently driven micromaser by the Monte Carlo wavefunction approach

Using a Monte Carlo wavefunction approach we investigate the dynamics of a micromaser driven by a resonant coherent field. At steady state, for increasing interaction times, the system exhibits driven Rabi oscillations, followed by collapse as the range of micromaser trapping states is approached. The system operates in regimes ranging from a strong to a weak amplifier. In the strong-amplifier regime the cavity mode shows a preferred phase and can exhibit quadrature squeezing and sub-Poissonian photon statistics. In the weak-amplifier regime the cavity mode has no preferred phase, is super-Poissonian and is influenced by trapping effects; no revival of Rabi oscillations occurs. The main predictions can be compared with experimental measurements on the populations of atoms leaving the cavity.

Dynamic generation of maximally entangled photon multiplets by adiabatic passage

The adiabatic passage scheme for quantum state synthesis, in which atomic Zeeman coherences are mapped to photon states in an optical cavity, is extended to the general case of two degenerate cavity modes with orthogonal polarization. Analytical calculations of the dressed-state structure and Monte Carlo wave-function simulations of the system dynamics show that, for a suitably chosen cavity detuning, it is possible to generate states of photon multiplets that are maximally entangled in polarization. These states display nonclassical correlations of the type described by Greenberger, Horne, and Zeilinger (GHZ). An experimental scheme to realize a GHZ measurement using coincidence detection of the photons escaping from the cavity is proposed. The correlations are found to originate in the dynamics of the adiabatic passage and persist even if cavity decay and GHZ state synthesis compete on the same time scale. Beyond entangled field states, it is also possible to generate entanglement between photons and the atom by using a different atomic transition and initial Zeeman state.

Optimization of quantum Monte Carlo wave functions using analytical energy derivatives

An algorithm is proposed to optimize quantum Monte Carlo (QMC) wave functions based on Newton’s method and analytical computation of the first and second derivatives of the variational energy. This direct application of the variational principle yields significantly lower energy than variance minimization methods when applied to the same trial wave function. Quadratic convergence to the local minimum of the variational parameters is achieved. A general theorem is presented, which substantially simplifies the analytic expressions of derivatives in the case of wave function optimization. To demonstrate the method, the ground-state energies of the first-row elements are calculated.

Tunneling Dynamics and Gauge Potentials in Optical Lattices

We study periodic well-to-well tunneling of ${}^{87}\mathrm{Rb}$ atoms on adiabatic potential surfaces of a 1D optical lattice. The observed dependence of the lowest-band tunneling period on the depth of the adiabatic potential can only be explained by an additional intensity-independent gauge potential predicted by Dum et al. The experimental data are in excellent agreement with our quantum Monte Carlo wave-function simulations and band structure calculations.

Nuclear Structure Studies with the7Li(e,e′p)Reaction

Experimental momentum distributions for the transitions to the ground state and first excited state of {sup 6}He have been measured via the reaction {sup 7}Li( e,thinspe{prime}p){sup 6}He . They are compared to theoretical distributions calculated with variational Monte Carlo (VMC) wave functions which include strong state-dependent correlations in both {sup 7}Li and {sup 6}He . These VMC calculations provide a parameter-free prediction that reproduces the measured data, including its normalization. The deduced spectroscopic factor for the two transitions is 0.58{plus_minus}0.05 , in perfect agreement with the VMC value of 0.60. This is the first successful comparison of experiment and {ital ab initio} theory for spectroscopic factors in p -shell nuclei. {copyright} {ital 1999} {ital The American Physical Society}

Quantum-jump approach to dipole dephasing: Application to inversionless amplification

We present a model for simulating atomic dipole dephasing within the Monte-Carlo wave function formalism which leads to the same results as the standard density-matrix formalism. In this model dipole dephasing processes are accounted by quantum-jumps into one of the atomic energy eigenstates. This fact allows us to obtain analytical expressions for the effects of elastic collisions on the various physical processes responsible for amplification without population inversion in a cascade three-level atomic configuration.

Comment on “Resonance fluorescence near a photonic band edge: Dressed-state Monte Carlo wave-function approach”

Quang and John have, in a recent paper [Phys. Rev. A $56,$ 4273 (1997)], proposed a dressed-state Monte Carlo wave-function (MCWF) approach to a laser-driven two-level atom coupled to a structured radiation reservoir. In this Comment, we argue that this approach is at variance with the underlying physical idea of the MCWF technique, that it is at variance with basic formal requirements for the MCWF technique to apply, and that it produces spurious and unphysical quantitative results for wide ranges of parameters.

Stochastic Schrödinger equations in cavity QED: physical interpretation and localization

We propose physical interpretations for stochastic methods which have been developed recently to describe the evolution of a quantum system interacting with a reservoir. As opposed to the usual reduced density operator approach, which refers to ensemble averages, these methods deal with the dynamics of single realizations, and involve the solution of stochastic Schr\"odinger equations. These procedures have been shown to be completely equivalent to the master equation approach when ensemble averages are taken over many realizations. We show that these techniques are not only convenient mathematical tools for dissipative systems, but may actually correspond to concrete physical processes, for any temperature of the reservoir. We consider a mode of the electromagnetic field in a cavity interacting with a beam of two- or three-level atoms, the field mode playing the role of a small system and the atomic beam standing for a reservoir at finite temperature, the interaction between them being given by the Jaynes-Cummings model. We show that the evolution of the field states, under continuous monitoring of the state of the atoms which leave the cavity, can be described in terms of either the Monte Carlo Wave-Function (quantum jump) method or a stochastic Schr\"odinger equation, depending on the system configuration. We also show that the Monte Carlo Wave-Function approach leads, for finite temperatures, to localization into jumping Fock states, while the diffusion equation method leads to localization into states with a diffusing average photon number, which for sufficiently small temperatures are close approximations to mildly squeezed states.

Calculating Trajectories for Atoms in Near-resonant Lightfields

We review several methods for calculating the time development of the internal state and the external motion of atoms in near-resonant light fields, with emphasis on studying the focussing of atomic beams into microscopic and potentially nanoscopic patterns. Three different approaches are considered: two-level semiclassical, multi-level semiclassical, and the Monte Carlo wavefunction method. The two-level semiclassical technique of McClelland and Scheinfein (1991) and McClelland (1995) is extended to three dimensions, and used to calculate the trajectories of atoms and the imaging properties of a simple lens formed from a near-resonant travelling TEM01 mode laser. The model is then extended to multi-level atoms, where we calculate the density matrix for the internal state of a sample of thermal atoms in a standing wave, and show how cooling processes can be simulated. Finally, we use the Monte Carlo wavefunction method to calculate the internal state of the atom, and compare the results and required computation time to those of the multi-level semiclassical technique.

Microscopic Calculation ofL6iElastic and Transition Form Factors

Variational Monte Carlo wave functions, obtained from a realistic Hamiltonian consisting of the Argonne ${v}_{18}$ two-nucleon and Urbana-IX three-nucleon interactions, are used to calculate the ${}^{6}\mathrm{Li}$ ground-state longitudinal and transverse form factors as well as transition form factors to the first four excited states. The charge and current operators include one- and two-body components, leading terms of which are constructed consistently with the two-nucleon interaction. The calculated form factors and radiative widths are in good agreement with available experimental data.