Quantum kinetic theory model of a continuous atom laser

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.

Figure 1

Schematic of the experimental setup.

Figure 2

Schematic of processes involved in the evolution of the kinetic model described by (1): collisional processes involving (a) two thermal atoms and (b) one thermal and one condensate atom; (c) the change in the energy distribution function $g(\varepsilon ,t)$ if the condensate occupation (and hence chemical potential) increases, raising the energies of every energy level; (d) the replenishment of the thermal cloud from an atomic reservoir; (e) outcoupling from the condensate mode to produce the atom laser; and (f) the loss of atoms due to three-body recombination. The upper shaded rectangle in each panel represents the energy distribution function $g(\varepsilon ,t)$ of the thermal cloud, and the bottom dark blue rectangle represents the condensate with occupancy $N_0\left(t\right)$ and chemical potential $\varepsilon =\mu \left(t\right)$.

Figure 3

Results of the kinetic model for $\Phi =8.4\times {10}^5$ atoms/s, $T=540$ nK, ${\varepsilon }_{\mathrm{cut}}=3k_{B}T\approx 610\hslash \overline{\omega }$, and $\gamma =0.3$ s${}^{-1}$: (a) dynamics of the occupation of the thermal energy levels for $t<0.5$ s, and (b) the achievement of a steady state of the total and condensed atom numbers over $\sim$10 s. The energy distribution at $t=0$ is a truncated Bose-Einstein distribution containing (before truncation) $N=4.2\times {10}^6$ atoms at $T=540$ nK.

Figure 4

The dependence of the steady-state condensate number $N_0$ on the parameters of the quantum kinetic model (1). The steady-state condensate number has a monotonic dependence on (a) the replenishment flux $\Phi$, (b) the temperature $T$ of the replenishment source, and (c) the outcoupling rate $\gamma$. For a given choice of the remaining parameters of the model there is (d) an optimum ${\varepsilon }_{\mathrm{cut}}$ for which the steady-state condensate number is a maximum. For each parameter being varied, the remaining parameters are chosen to be the same as for the results depicted in Fig. 3. The triangle in each plot marks the point that corresponds to the precise conditions of Fig. 3 in steady state.

Figure 5

Steady-state condensate properties as a function of the phase-space flux $\kappa$ for the replenishment source: steady-state condensate number on (a) linear-linear and (b) log-log scales, and (c) steady-state condensate fraction $N_0/N$. The results of the parameter scan are divided into three groups (black circles, red triangles, and blue crosses) based on their proximity to the high-temperature limit, where $\kappa$ is expected to be the only figure of merit. The circled point with the arrow pointing to it corresponds to a simulation of the parameters for the last source in Table , which has $\kappa =1.1\times {10}^{-2}$ s${}^{-1}$ (see main text).