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Journal of Physics A Mathematical and General

Controlling quantum motions of a trapped and driven electron: an exact analytic treatment

Gengbiao Lu, Wenhua Hai, Qiongtao Xie

Published Dec 14, 2005• 12 citations
Publisher

Abstract

We consider a harmonically trapped and strongly driven electron in a one-dimensional (1D) quantum wire. A set of exact complete solutions of the time-dependent Schrödinger equation is constructed, which shows the properties of generalized squeezed coherent states. The corresponding probability densities behave like some breathing and oscillating wave-packet-trains. The resonance ladders of the expectation energy are found and the transition probabilities between two stationary states are exactly calculated. The results reveal that the quantum motions of the considered system can be controlled by adjusting the laser driving field.

DOI
10.1088/0305-4470/39/2/010

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We consider a harmonically trapped and strongly driven electron in a one-dimensional (1D) quantum wire. A set of exact complete solutions of the time-dependent Schrödinger equation is constructed, which shows the properties of generalized squeezed coherent states. The corresponding probability densities behave like some breathing and oscillating wave-packet-trains. The resonance ladders of the expectation energy are found and the transition probabilities between two stationary states are exactly calculated. The results reveal that the quantum motions of the considered system can be controlled by adjusting the laser driving field.
We have studied the quantum and classical motions of a single Paul trapped ion interacting with a time-periodic laser field. By using the test-function method, we construct n exact solutions of quantum dynamics that describe the generalized squeezed coherent states with the expectation orbits being the corresponding classical ones. The space-time evolutions of the exact probability densities show some wavepacket trains. It is demonstrated analytically that by adjusting the laser intensity and frequency, we can control the center motions of the wavepacket trains. We also discuss the other physical properties such as the expectation value of energy, the widths and heights of the wavepackets, and the resonance loss of stability.
By using an analytical method,exact solutions of the equation for a single tapped electron adiabatically interacting with an external field is obtained.Such exact solutions describe a series of exact squeezed coherent states of this quantum system,whose configuration of probability density is breathing and oscillatory wave-packets.The time evolutions of the expectation of coordinate,momentum and energy are greatly affected by the adiabatic factor in a time interval.Therefore,manipulation of quantum state can be realized by suitably adjusting adiabatic parameters.
We investigate the quantum motion of two ions stored in a Paul trap and interacting with a time-periodic laser field. In the pseudopotential approximation and large detuning condition, we find that the relative motion is independent of the laser field, but the exact centre-of-mass motion is closely related to the laser field. By adjusting the laser intensity and frequency, we can well control the quantum motion of the centre-of-mass. We illustrate some physical properties described by the centre-of-mass states, such as the squeezed coherent property, the widths and heights of the wavepackets of probability density, the classical-quantum correspondence, the resonance ladders of expectation energy and the transition probabilities between time-dependent quantum levels.
We investigate the dynamics of a charged particle interacting with a multimode quantized electromagnetic field and obtain an analytic solution for the full electron--field system. This framework enables the calculation of position expectation values and uncertainties for arbitrary wave packets and field states, allowing us to identify quantum corrections to the corresponding classical motion. While the corrections to the position expectation value are weak and largely insensitive to the quantum state of the field, the wave packet broadening exhibits a pronounced dependence on the field state. In particular, the quantum uncertainty of the radiation is directly imprinted onto the spatial uncertainty of the particle. We illustrate these effects for Gaussian wave packets interacting with coherent, Fock, and squeezed states, including bright squeezed vacuum. The interaction with a finite-duration laser pulse is also analyzed as a multimode example. Our results provide a transparent analytic route toward understanding how quantum fluctuations of light influence electron dynamics in strong-field settings.
A single particle magneto-confined in a one-dimensional (1D) quantum wire experiences a harmonic potential, and imposing a sharply focused laser beam on an appropriate site shapes a δ potential. The theoretical investigation has demonstrated that for a sufficiently strong δ pulse the quantum motional stationary state of the particle is one of the eigenstates of the free harmonic oscillator, and it is determined by the site of the laser beam uniquely, namely a quantum state is admissible if and only if the laser site is one of its nodes. The numerical computation shows that all the nodes of the lower energy states with quantum numbers n ≤ 20, except the coordinate origin, are mutually different. So we can manipulate the multiphoton transitions between the quantum states by adjusting the position of the laser δ pulse and realize the transition from an unknown higher excitation state to a required lower energy state.
We investigate the secular motion of a single Paul-trapped ion in the Lamb-Dicke regime, which interacts with a sequence of standing laser pulses. By using the ansatz method, we get an exact quantum solution of the system. Based on the wave-packet trains described by the exact solution, we find that: i) The center, height and width of the wave-packet trains depend on the strength of laser pulses, the deformation and spread of the wave-packet trains can be controlled by adjusting the strength of laser. ii) Energy expectation values of the ion show jumps at the instantaneous switching on of the laser pulses. In the time intervals when the laser pulses are switched off some narrow energy bands are generated. iii) When the strength of laser pulses reaches a critical value, the system changes its stability.