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arXiv:quant-ph/0212068 · Physical Review A

Trapping atoms in the vacuum field of a cavity

Christian Schön, J. I. Cirac

Published Apr 22, 2003• 8 citations
arXivHTMLPDF

Abstract

The aim of this work is to find ways to trap an atom in a cavity. In contrast to other approaches, we propose a method where the cavity is basically in the vacuum state and the atom is in the ground state. The idea is to induce a spatial dependent ac-Stark shift by irradiating the atom with a weak laser field, so that the atom experiences a trapping force. The main feature of our setup is that dissipation can be strongly suppressed. We estimate the lifetime of the atom as well as the trapping potential parameters, and compare our estimations with numerical simulations.

DOI
10.1103/physreva.67.043813

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The aim of this work is to find ways to trap an atom in a cavity. In contrast to other approaches, we propose a method where the cavity is basically in the vacuum state and the atom is in the ground state. The idea is to induce a spatial dependent ac-Stark shift by irradiating the atom with a weak laser field, so that the atom experiences a trapping force. The main feature of our setup is that dissipation can be strongly suppressed. We estimate the lifetime of the atom as well as the trapping potential parameters, and compare our estimations with numerical simulations.
We consider the situation where a two-level atom is placed in the vicinity of the center of a spherical cavity with a large numerical aperture. The vacuum field at the center of the cavity is actually equivalent to the one obtained in a microcavity, and both the dissipative and the reactive parts of the atom's spontaneous emission are significantly modified. Using an explicit calculation of the spatial dependence of the radiative relaxation rate and of the associated level shift, we show that for a weakly excitating light field, the atom can be attracted to the center of the cavity by vacuum-induced light shifts.
Two recent experiments have reported the trapping of individual atoms inside optical resonators by the mechanical forces associated with single photons [Hood et al., Science 287, 1447 (2000); Pinkse et al., Nature (London) 404, 365 (2000)]. Here we analyze the trapping dynamics in these settings, focusing on two points of interest. First, we investigate the extent to which light-induced forces in these experiments are distinct from their free-space counterparts, and whether or not there are qualitatively different effects of optical forces at the single-photon level within the setting of cavity QED. Second, we explore the quantitative features of the resulting atomic motion, and how these dynamics are mapped onto experimentally observable variations of the intracavity field. Toward these ends, we present results from extensive numerical simulations of the relevant forces and their fluctuations, as well as a detailed derivation of our numerical simulation method, based on the full quantum-mechanical master equation. Not surprisingly, qualitatively distinct atomic dynamics arise as the coupling and dissipative rates are varied. For the experiment of Hood et al., we show that atomic motion is largely conservative and is predominantly in radial orbits transverse to the cavity axis. A comparison with the free-space theory demonstrates that the fluctuations of the dipole force are suppressed by an order of magnitude. This effect is based upon the Jaynes-Cummings eigenstates of the atom-cavity system and represents distinct physics for optical forces at the single-photon level within the context of cavity QED. By contrast, even in a regime of strong coupling in the experiment of Pinkse et al., there are only small quantitative distinctions between the potentials and heating rates in the free-space theory and the quantum theory, so it is not clear that a description of this experiment as a novel single-quantum trapping effect is necessary. The atomic motion is strongly diffusive, leading to an average localization time comparable to the time for an atom to transit freely through the cavity, and to a reduction in the ability to infer aspects of the atomic motion from the intracavity photon number.
We analyse the force on an atom resonantly coupled to the vacuum field in a high-Q microwave cavity. The atom is prepared in the upper level of the atomic transition coupled to the cavity mode. The force results from the reversible exchange of a single excitation between the atom and the cavity. It derives from a potential which reflects the spatial variations of the r.m.s. vacuum field inside the cavity. Depending upon the atom-cavity dressed state into which the system is prepared, this potential presents either a maximum or a minimum at the point where vacuum fluctuations are largest. Very slow circular Rydberg atoms may be reflected back as they enter the cavity, or trapped around cavity centre.
A robust scheme for trapping and cooling atoms is described. It combines a deep dipole-trap which localizes the atom in the center of a cavity with a laser directly exciting the atom. In that way one obtains three-dimensional cooling while the atom is dipole-trapped. In particular, we identify a cooling force along the large spatial modulations of the trap. A feature of this setup, with respect to a dipole trap alone, is that all cooling forces keep a constant amplitude if the trap depth is increased simultaneously with the intensity of the probe laser. No strong coupling is required, which makes such a technique experimentally attractive. Several analytical expressions for the cooling forces and heating rates are derived and interpreted by analogy to ordinary laser cooling.
Quantum vacuum forces dictate the interaction between individual atoms and dielectric surfaces at nanoscale distances. For example, their large strengths typically overwhelm externally applied forces, which makes it challenging to controllably interface cold atoms with nearby nanophotonic systems. Here we theoretically show that it is possible to tailor the vacuum forces themselves to provide strong trapping potentials. Our proposed trapping scheme takes advantage of the attractive ground-state potential and adiabatic dressing with an excited state whose potential is engineered to be resonantly enhanced and repulsive. This procedure yields a strong metastable trap, with the fraction of excited-state population scaling inversely with the quality factor of the resonance of the dielectric structure. We analyse realistic limitations to the trap lifetime and discuss possible applications that might emerge from the large trap depths and nanoscale confinement. Atoms experience large and typically undesirable forces near dielectric surfaces due to quantum fluctuations of the electromagnetic vacuum. The work of Chang et al.proposes a scheme in which these forces can be exploited to create strong atomic traps at nanoscale distances from surfaces.
Single cesium atoms are cooled and trapped inside a small optical cavity by way of a novel far-off-resonance dipole-force trap, with observed lifetimes of 2−−3 s2--3\text{ }\mathrm{s}2−−3 s. Trapped atoms are observed continuously via transmission of a strongly coupled probe beam, with individual events lasting $\ensuremath{\simeq}1\text{ }\text{ }\mathrm{s}$. The loss of successive atoms from the trap $N\ensuremath{\ge}3\ensuremath{\rightarrow}2\ensuremath{\rightarrow}1\ensuremath{\rightarrow}0$ is thereby monitored in real time. Trapping, cooling, and interactions with strong coupling are enabled by the trap potential, for which the center-of-mass motion is only weakly dependent on the atom's internal state.