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Quantum Electronics and Laser Science Conference

Self-sustained hysteretic motional oscillations of a single atom pumped by a laser standing wave

A. E. Kaplan

Published Jan 20, 2003• 0 citations
Publisher

Abstract

Summary form only given. Self-sustained oscillations/oscillators (SSO), man-made or naturally occurring, are some of the most universal phenomena. The common feature of all SSO is the so called positive feedback, which overcomes the damping by properly controlling the energy supply (pumping) from the outside source during the cycle of oscillations. Usually, the zero steady-state point of the system is unstable, and the oscillations grow up till they reach a stable limit cycle. The common quality of the resulting SSO is their well defined amplitude (the so called classical squeezing) at the expense of undetermined phase of oscillations. All the "mechanical motion" SSO known so far, were based on macro-systems, while it would be of great importance to develop a microscopic SS-oscillator based on a single particle (atom or ion), which would enable us to control the SSO mode from classical to quantum limits. The effect proposed is based on the interaction of a standing laser wave with an atom moving in along the laser beam propagation. If the laser beam is red-shifted with respect to the resonant absorption line of the atom at rest, the moving atom will experience deaccelerating force induced by a standing wave due to combinations of Doppler shifts in counterpropagating waves; this effect is at the core of laser cooling of atoms. On the other hand, if the laser wave is blue-shifted, the atom will undergo acceleration (positive feedback) in the laser field due to the Doppler-shift, which can be used for excitation of atomic SSO.

DOI
10.1109/qels.1999.807325

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~Received 30 October 1996! We observe quantum tunneling of cold sodium atoms from an accelerating one-dimensional standing wave of light. Atoms are trapped in a far-detuned standing wave that is accelerated for a controlled duration. For sufficiently large values of the acceleration, we observe an exponential decay in the number of atoms that remain trapped as a function of the interaction time. We show that this loss is due to quantum tunneling, and compare the decay rates with Landau-Zener theory. We also observe oscillations in the tunneling rate as a function of the acceleration which are due to quantum interference effects. @S1050-2947~97!50702-5# PACS number~s!: 03.75.Be, 32.80.Pj, 42.50.Vk Tunneling in the center-of mass motion of atoms should become an important process at the low temperatures that are now achieved with laser cooling. This can appear, for example, as a loss mechanism for atoms confined in an optical lattice constructed from interfering beams of light. While atomic motion in these structures has become an active area of research @1,2#, tunneling has been obscured by spontaneous scattering @3#. An alternative atom optics system where tunneling can be significant has appeared in our efforts to develop a cold atomic beam for interferometry. Our approach has been to launch laser-cooled atoms in the potential created by an accelerating, far-detuned, standing wave of light. This system was previously used to study Wannier-Stark ladders @4# and Bloch oscillations @5#. The results reported in this Rapid Communications provide an observation of tunneling in atom optics, and the high degree of experimental control has enabled a quantitative comparison with theory. We consider atomic motion in an accelerating standing wave of light. For sufficiently large detuning from atomic resonance, the atoms remain in their internal ground state and experience an effective one-dimensional potential given by V0cos@2kL(x2at 2 /2)#, where k L52p/l L is the wave number, and a is the acceleration of the standing wave @6#. The well depth V0 is the amplitude of the optical dipole potential. It is proportional to the laser intensity and inversely proportional to detuning from atomic resonance. We neglect variations of the potential in the two transverse directions, which is justified for beams that are sufficiently

Quantum Electronics and Laser Science Conference•Jan 1, 1997•0 citations
Summary form only given. Self-sustained oscillations/oscillators (SSO), man-made or naturally occurring, are some of the most universal phenomena. The common feature of all SSO is the so called positive feedback, which overcomes the damping by properly controlling the energy supply (pumping) from the outside source during the cycle of oscillations. Usually, the zero steady-state point of the system is unstable, and the oscillations grow up till they reach a stable limit cycle. The common quality of the resulting SSO is their well defined amplitude (the so called classical squeezing) at the expense of undetermined phase of oscillations. All the "mechanical motion" SSO known so far, were based on macro-systems, while it would be of great importance to develop a microscopic SS-oscillator based on a single particle (atom or ion), which would enable us to control the SSO mode from classical to quantum limits. The effect proposed is based on the interaction of a standing laser wave with an atom moving in along the laser beam propagation. If the laser beam is red-shifted with respect to the resonant absorption line of the atom at rest, the moving atom will experience deaccelerating force induced by a standing wave due to combinations of Doppler shifts in counterpropagating waves; this effect is at the core of laser cooling of atoms. On the other hand, if the laser wave is blue-shifted, the atom will undergo acceleration (positive feedback) in the laser field due to the Doppler-shift, which can be used for excitation of atomic SSO.
Abstract Self-sustained oscillators (SSOs) is a commonly used method to generate classical clock signals and SSOs using delayed feedback have been developed commercially which possess ultra-low phase noise and drift. Research into the development of quantum self-oscillation, where one can also have a periodic and regular output tick, that can be used to control quantum and classical devices has received much interest and quantum SSOs so far studied suffer from phase diffusion which leads to the smearing out of the quantum oscillator over the entire limit cycle in phase space seriously degrading the system’s ability to perform as a self-oscillation. In this paper, we explore quantum versions of time-delayed SSOs, which has the potentials to develop a ticking quantum clock. We first design a linear quantum SSO which exhibits perfect oscillation without phase diffusion. We then explore a nonlinear delayed quantum SSO but find it exhibits dephasing similar to previously studied non-delayed systems.
We study a single incoherently pumped atom moving within an optical high-QQQ resonator in the strong-coupling regime. Using a semiclassical description for the atom and field dynamics, we derive a closed system of differential equations to describe this coupled atom-field dynamics. For sufficiently strong pumping, the system starts lasing when the atom gets close to a field antinode, and the associated light forces provide for self-trapping of the atom. For a cavity mode blue detuned with respect to the atomic transition frequency, this is combined with cavity-induced motional cooling, allowing for long-term steady-state operation of such a laser. The analytical results for temperature and field statistics agree well with our earlier predictions based on quantum Monte Carlo simulations. We find sub-Doppler temperatures that decrease with gain and coupling strength, and can even go beyond the limit of passive cavity cooling. Besides demonstrating the importance of light forces in single-atom lasers, this result also gives strong evidence to enhance laser cooling through stimulated emission in resonators.
The analysis of atomic motion in the field formed by sequences of counterpropagating light pulses reveals the conditions when the field creates the trap in which the temperature of trapped atoms drops to the Doppler limit. The atomic state is described by the wave function using the Monte Carlo wave function method, whereas the atomic motion is considered in the framework of classical mechanics. Laser cooling and trapping is achieved only for non-resonant atom–field interaction. The pulse area does not matter for this effect, in contrast to the repetition period. When the motion of a trapped atom is slowed down, it oscillates around the anti-nodes of a non-stationary standing wave formed by the counterpropagating light pulses at the point where they ‘collide’. The discussed trap is also applicable for trapping and cooling of the molecules for which the matrix of Frank–Condon factors is almost diagonal.
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.
~Received 30 October 1996! We observe quantum tunneling of cold sodium atoms from an accelerating one-dimensional standing wave of light. Atoms are trapped in a far-detuned standing wave that is accelerated for a controlled duration. For sufficiently large values of the acceleration, we observe an exponential decay in the number of atoms that remain trapped as a function of the interaction time. We show that this loss is due to quantum tunneling, and compare the decay rates with Landau-Zener theory. We also observe oscillations in the tunneling rate as a function of the acceleration which are due to quantum interference effects. @S1050-2947~97!50702-5# PACS number~s!: 03.75.Be, 32.80.Pj, 42.50.Vk Tunneling in the center-of mass motion of atoms should become an important process at the low temperatures that are now achieved with laser cooling. This can appear, for example, as a loss mechanism for atoms confined in an optical lattice constructed from interfering beams of light. While atomic motion in these structures has become an active area of research @1,2#, tunneling has been obscured by spontaneous scattering @3#. An alternative atom optics system where tunneling can be significant has appeared in our efforts to develop a cold atomic beam for interferometry. Our approach has been to launch laser-cooled atoms in the potential created by an accelerating, far-detuned, standing wave of light. This system was previously used to study Wannier-Stark ladders @4# and Bloch oscillations @5#. The results reported in this Rapid Communications provide an observation of tunneling in atom optics, and the high degree of experimental control has enabled a quantitative comparison with theory. We consider atomic motion in an accelerating standing wave of light. For sufficiently large detuning from atomic resonance, the atoms remain in their internal ground state and experience an effective one-dimensional potential given by V0cos@2kL(x2at 2 /2)#, where k L52p/l L is the wave number, and a is the acceleration of the standing wave @6#. The well depth V0 is the amplitude of the optical dipole potential. It is proportional to the laser intensity and inversely proportional to detuning from atomic resonance. We neglect variations of the potential in the two transverse directions, which is justified for beams that are sufficiently