Non-Markovian Particle Dynamics in Continuously Controlled Quantum Gases

For a quantum gas, being subject to continuous feedback of a macroscopic observable, the single-particle dynamics is studied. Despite feedback-induced particle correlations, it is shown that analytic solutions are obtained by formally extending the single-particle Hilbert space by an auxiliary degree of freedom. The particle’s motion is then fed by colored noise, which effectively maps quantum-statistical correlations onto the single particle. Thus, the single particle in the continuously controlled gas follows a non-Markovian trajectory in phase space.

Figure 1

Noise spectrum for ${\alpha }_N<1/\sqrt{2}$ (${\alpha }_N=1/2$) for the case satisfying Eq. (14) with $\eta =\sqrt{2}$ (solid line), and for $\eta =1/\sqrt{2}$ (dashed line).

Figure 2

Noise spectrum for ${\alpha }_N>1/\sqrt{2}$ ($\eta =1/\sqrt{2}$), for the oscillatory case ${\alpha }_N=0.8$ (solid line) and the over-damped case ${\alpha }_N=1.25$ (dashed line).