Reducing the Linewidth of an Atom Laser by Feedback

Abstract

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 non-demolition measurement of the atom number of the condensate in situ can reduce the linewidth enormously. 03.75.Fi, 42.50.Lc An atom laser is a continuous source of coherent atom waves, analogous to an ordinary laser which is a continuous source of coherent photon waves (light) [1,2]. Ideas for creating an atom laser were published independently by a number of authors [3][4][5][6], shortly after the first achievement of Bose-Einstein condensation (BEC) of gaseous atoms [7][8][9]. There have since been some important advances in the coherent release of pulses [10,11] and beams [12,13] of atoms from a condensate. Since the condensate is not replenished in these experiments, the output coupling cannot continue indefinitely [14]. Nevertheless they represent major steps towards achieving a continuously operating atom laser.The coherence of an atom laser beam can be defined analogously to that of an optical laser beam: the atoms should have a relatively small longitudinal momentum spread, they should ideally be restricted to a single transverse mode and internal state, and their flux should be relatively constant [2]. A fourth condition, rarely considered for optical lasers because it is so easily satisfied, is that the laser beam be Bose degenerate. This requires that the atom flux be much larger than the linewidth (the reciprocal of the coherence time) [2]. A crucial contributor to the linewidth of an atom laser is the collisional interaction of atoms, which is negligible for photons. This is difficult to avoid because it is the collisions between atoms that enables BEC by evaporative cooling, at present the only method for achieving an atom laser.In this Letter we show that using a feedback mechanism can reduce the effect of atomic interactions on the atom laser linewidth by a factor as large as the square root of the atom number. For a single-mode condensate the dominant effect of collisions is to turn atom number fluctuations in the condensate into fluctuations in the energy, which are equivalent to frequency fluctuations. By monitoring the number fluctuations, it is possible using feedback to largely compensate for the linewidth caused by these frequency fluctuations. The key practical points are that the measurement does not rely upon any external condensate phase reference, and that the control requires only the ability to change the energy of the atoms, which could be done with a spatially uniform optical or magnetic field.We begin by deriving the standard laser linewidth (for non-interacting bosons) using a simple method which is applied to all later ca...

Atom-laser coherence and its control via feedback

“…(3.8), except at the boundary between the regimes. This is illustrated by the figure in our previous paper [20], and also the extended version in this paper, Fig. 2 appearing in Sec.…”

“…Collisional interactions therefore lead to a significant decrease in the atom-laser coherence time, and a corresponding increase in the linewidth, especially in the case of BECs formed by evaporative cooling. However, we have previously shown that a continuous, quantum nondemolition (QND) feedback scheme can effectively cancel the linewidth broadening due to such collisions [20].…”

Stability of Continuously Pumped Atom Lasers

“…This effect is not dependent on the output coupling, but could possibly be controlled by a highly mode selective pumping mechanism. This result is important in the design of continuously pumped atom lasers because the Kerr-like phase diffusion will scale with the interactions, and will induce a fundamental limit to the linewidth of the atom laser beam [14]. Because of the opposite scaling of the semiclassical and the quantum noise, if an atom laser can be operated in a stable regime then we expect it to have a minimum linewidth at an optimum scattering length.…”

“…It is also extremely difficult to include the effects of the atomic interactions in these models. Atom laser linewidths will be limited by these interactions due to Kerr-like dephasing of the lasing mode [14], as well as by thermal effects [15].…”

How measurement reversal could erroneously suggest the capability to discriminate the preparation basis of a quantum ensemble

“…In this paper we present a measurement scheme * sandeep.goyal@ucalgary.ca that would appear to violate this idea; i.e., we appear to distinguish between two preparation methods. This measurement scheme uses unsharp measurements that are also known as positive operator valued measurements (POVMs) [7][8][9][10]. We present a special class of POVMs that can cause the recurrence of the original state of the quantum system upon repeated measurements.…”