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Chinese Physics

Laser-manipulated the multiphoton transitions of a harmonically trapped particle

Qiong Chen, Hai Kuo, Hai Wen-Hua

Published Dec 1, 2007• 2 citations
Publisher

Abstract

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.

DOI
10.1088/1009-1963/16/12/018

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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.
Laser cooling in a trap is investigated for laser and trapping configurations which allow the existence of approximate ``dark states'' of the combined atom-plus-trap system, i.e., states that are decoupled from the laser light by quantum interference. We show that a one-dimensional (1D) free-particle dark state in angular momentum Jg{\mathit{J}}_{\mathit{g}}Jg​=1 to Je{\mathit{J}}_{\mathit{e}}Je​=1 transitions and in two counterpropagating laser fields survives as an approximate dark state in a ``flat-bottom'' trap of size much larger than the optical wavelength. Furthermore, we show the existence of approximate dark states in 1D harmonic-oscillator potentials. In the latter configuration we are able to provide analytical results.
We propose a scheme to investigate the nonequilibrium work distribution of a quantum particle under well controlled transformations of the external potential, exploiting the versatility of a single ion in a segmented linear Paul trap. We describe in detail how the motional quantum state of a single ion can be prepared, manipulated, and finally readout to fully determine the free energy difference in both harmonic and anharmonic potentials. Uniquely to our system, we show how an ion may be immersed in an engineered laser-field reservoir. Trapped ions therefore represent an ideal tool for investigating the Jarzynski equality in open and closed quantum systems.
In quantum physics the free particle and the harmonically trapped particle are arguably the most important systems a physicist needs to know about. It is little known that, mathematically, they are one and the same. This knowledge helps us to understand either from the viewpoint of the other. Here we show that all general time-dependent solutions of the free-particle Schrödinger equation can be mapped to solutions of the Schrödinger equation for harmonic potentials, both the trapping oscillator and the inverted “oscillator”. This map is fully invertible and therefore induces an isomorphism between both types of system, they are equivalent. A composition of the map and its inverse allows us to map from one harmonic oscillator to another with a different spring constant and different center position. The map is independent of the state of the system, consisting only of a coordinate transformation and multiplication by a form factor, and can be chosen such that the state is identical in both systems at one point in time. This transition point in time can be chosen freely, the wave function of the particle evolving in time in one system before the transition point can therefore be linked up smoothly with the wave function for the other system and its future evolution after the transition point. Such a cut-and-paste procedure allows us to describe the instantaneous changes of the environment a particle finds itself in. Transitions from free to trapped systems, between harmonic traps of different spring constants or center positions, or, from harmonic binding to repulsive harmonic potentials are straightforwardly modelled. This includes some time-dependent harmonic potentials. The mappings introduced here are computationally more efficient than either state-projection or harmonic oscillator propagator techniques conventionally employed when describing instantaneous (non-adiabatic) changes of a quantum particle’s environment.
The force acting on a two-level atom in a low-intensity standing laser wave is calculated. On account of this force, atoms can be trapped at the loops (antinodes) of the field. By quantizing the atomic motion near the bottom of the sinusoidal potential, we have studied the atomic behavior when they are trapped in bound states as well as when they are in the free state. Laser cooling of neutral atoms was first suggested by T. Hansh and A. Schawlow in 1975. The principle involves the Doppler effect in a detuned laser beam. The absorption rate of a photon depends on the apparent frequency of the photon that is shifted ωv/c\omega v/cωv/c from ω\omegaω, where ω\omegaω is the frequency of the laser, v is the velocity of the atom, and c is the velocity of light. For a single laser beam detuned slightly below an atomic resonance frequency, the apparent frequency for atoms moving toward the laser is closer to resonance, which causes a higher absorption rate. And these atoms lose momentum when they absorb a photon from the beam. The velocity of atoms can be decreased from 10$\sp5$ cm/sec, the velocity they have when they escape from an oven, to 10$\sp2$ cm/sec (about 1mK) by a laser beam. For further cooling, counterpropagating beams are necessary. In this study we propose a new mechanism for supercooling, that is, cooling well below the Doppler cooling limit. Within a standing laser wave there exists a force called a "dipole force", which has a sinusoidal spatial dependence. Once atoms are trapped by the potential, their motion around the minimum of the potential well is that of a simple harmonic oscillator. Restricting our attention to the two lowest quantized states, we calculate transition rates between free states and bound states, from which the average residence times in the bound states can be obtained. This first quantum treatment of an atom trapped in the sinusoidal potential is restricted to the one-dimensional case. Generalization to higher dimensions is left for future research.
It is shown that general solutions of the free-particle Schroedinger equation can be mapped onto solutions of the Schroedinger equation for the harmonic oscillator. This is done in such a way that the time evolution of a free particle subjected to a sudden transition to a harmonic potential can be described by a simple coordinate transformation applied at the transition time. This procedure is computationally more efficient than either state-projection or propagator techniques. A concatenation of the map and its inverse allows us to map from one harmonic oscillator to another with a different spring constant.
We present a study of Doppler-sensitive light-pulse atom interferometers operating within optical dipole potentials, where atomic trajectories are manipulated using momentum transfer from light pulses and optical forces from the trap. Efficient methods are introduced to minimize the inhomogeneous broadening of oscillation frequencies in atoms confined within a three-dimensional optical lattice trap. These techniques enable the preparation of various quantum states, including vacuum, thermal, and squeezed states, for atom interferometry. Additionally, we demonstrate a two-dimensional atom interferometer using a single optical dipole trap, where transverse motion is activated by offsetting the trap position. Our work provides insights into controlling the mechanical motion of neutral atoms in optical harmonic potentials and contributes to advancing applications in quantum sensing and quantum computing.