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arXiv:quant-ph/0612189 · Physical Review A

Semiclassical limits to the linewidth of an atom laser

Mattias Johnsson, Simon A. Haine, J. J. Hope, Nicholas P. Robins, C. Figl, Matthew Jeppesen, Julien Dugué, J. D. Close

Published Apr 20, 2007• 21 citations
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Abstract

We investigate the linewidth of a quasicontinuous atom laser within a semiclassical framework. In the high flux regime, the lasing mode can exhibit a number of undesirable features such as density fluctuations. We show that the output therefore has a complicated structure that can be somewhat simplified using Raman outcoupling methods and energy-momentum selection rules. In the weak outcoupling limit, we find that the linewidth of an atom laser is instantaneously Fourier limited, but, due to the energy ``chirp'' associated with depletion of the condensate, the long-term linewidth of an atom laser is equivalent to the chemical potential of the condensate source. We show that correctly sweeping the outcoupling frequency can recover the Fourier-limited linewidth.

DOI
10.1103/physreva.75.043618

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We investigate the linewidth of a quasicontinuous atom laser within a semiclassical framework. In the high flux regime, the lasing mode can exhibit a number of undesirable features such as density fluctuations. We show that the output therefore has a complicated structure that can be somewhat simplified using Raman outcoupling methods and energy-momentum selection rules. In the weak outcoupling limit, we find that the linewidth of an atom laser is instantaneously Fourier limited, but, due to the energy ``chirp'' associated with depletion of the condensate, the long-term linewidth of an atom laser is equivalent to the chemical potential of the condensate source. We show that correctly sweeping the outcoupling frequency can recover the Fourier-limited linewidth.
A continuous-wave atom laser formed by the outcoupling of atoms from a trapped Bose-Einstein condensate (BEC) potentially has a range of metrological applications. However, in order for the device to be truly continuous, a mechanism to replenish the atoms in the BEC is required. Here we calculate the temporal coherence properties of a continuously pumped atom laser beam outcoupled from a trapped Bose-Einstein condensate that is replenished from a reservoir at finite temperature. We find that the thermal fluctuations of the condensate can significantly decrease the temporal coherence of the output beam due to atomic interactions between the trapped BEC and the beam, and this can impact the metrological usefulness of the device. We demonstrate that a Raman outcoupling scheme imparting a sufficient momentum kick to the atom laser beam can lead to a significantly reduced linewidth.
The linewidth of an atom laser can be limited by excitation of higher energy modes in the source Bose-Einstein condensate, energy shifts in that condensate due to the atomic interactions, or phase diffusion of the lasing mode due to those interactions. The first two are effects that can be described with a semiclassical model, and have been studied in detail for both pumped and unpumped atom lasers. The third is a purely quantum statistical effect and has been studied only in zero-dimensional models. We examine an unpumped atom laser in one dimension using a quantum field theory using stochastic methods based on the truncated Wigner approach. This allows spatial and statistical effects to be examined simultaneously, and the linewidth limit for unpumped atom lasers is quantified in various limits.
If atom lasers are to transform many fields of physics, as well as find applications in industry, the most essential development needed is increased atom flux. In this thesis we report on the experimental observation of fundamental limits on the flux of continuous atom lasers. The flux produced by the commonly used radio frequency outcoupler, can not be arbitrarily increased by increasing the strength of the outcoupling. Above a critical Rabi frequency, the atom laser shows large classical density fluctuations, due to coupling between the multiple Zeeman states. In our system this critical Rabi frequency is about 1 kHz. Futhermore, at large coupling strengths (> 4 kHz for our experimetnal parameters), the continuous atom laser output completely switches off, as a result of the atoms remaining trapped in a bound state. In addition to the investigations of the radio frequency outcoupler, we have demonstrated the first continuous Raman outcoupled atom laser. Preliminary data indicates that the Raman outcoupler will be flux limited in a similar way to the radio frequency outcoupler.
A continuous atom laser will almost certainly have a linewidth dominated by the effect of the atomic interaction energy, which turns fluctuations in the condensate atom number into fluctuations in the condensate frequency. These correlated fluctuations mean that information about the atom number could be used to reduce the frequency fluctuations, by controlling a spatially uniform potential. We show that feedback based on a physically reasonable quantum nondemolition measurement of the atom number of the condensate in situ can reduce the linewidth enormously.
We investigate the feasible limits for realizing a continuously evaporated atom laser with high-temperature sources. A plausible scheme for realizing a truly continuous atom laser is to outcouple atoms from a partially condensed Bose gas while continuously reloading the system with noncondensed thermal atoms and performing evaporative cooling. Here we use quantum kinetic theory to model this system and estimate feasible limits for the operation of such a scheme. For sufficiently high temperatures, the figure of merit for the source is shown to be the phase-space flux. The dominant process limiting the usage of sources with low phase-space flux is the three-body loss of the condensed gas. We conclude that certain double-magneto-optical trap sources may produce substantial mean condensate numbers through continuous evaporation and provide an atom laser source with a narrow linewidth and reasonable flux.
Background: Theoretical studies of superradiant lasing on optical clock transitions predict a superb frequency accuracy and precision closely tied to the bare atomic linewidth. Such a superradiant laser is also robust against cavity fluctuations when the spectral width of the lasing mode is much larger than that of the atomic medium. Recent predictions suggest that this unique feature persists even for a hot and thus strongly broadened ensemble, provided the effective atom number is large enough. Methods: Here we use a second-order cumulant expansion approach to study the power, linewidth and lineshifts of such a superradiant laser as a function of the inhomogeneous width of the ensemble including variations of the spatial atom-field coupling within the resonator. Results: We present conditions on the atom numbers, the pump and coupling strengths required to reach the buildup of collective atomic coherence as well as scaling and limitations for the achievable laser linewidth. Conclusions: We show how sufficiently large numbers of atoms subject to strong optical pumping can induce synchronization of the atomic dipoles over a large bandwidth. This generates collective stimulated emission of light into the cavity mode leading to narrow-band laser emission at the average of the atomic frequency distribution. The linewidth is orders of magnitudes smaller than that of the cavity as well as the inhomogeneous gain broadening and exhibits reduced sensitivity to cavity frequency noise.