Fluctuations of the order parameter of a mesoscopic Floquet condensate

We suggest that nonequilibrium Bose-Einstein condensates may occur in time-periodically driven interacting Bose gases. Employing the model of a periodically forced bosonic Josephson junction, we demonstrate that resonance-induced ground-state-like many-particle Floquet states possess an almost perfect degree of coherence, as corresponding to a mesoscopically occupied, explicitly time-dependent single-particle orbital. In marked contrast to the customary time-independent Bose-Einstein condensates, the order parameter of such systems is destroyed by violent fluctuations when the particle number becomes too large, signaling the nonexistence of a proper mean-field limit.

Figure 1

Degree of coherence (6) for the lowest five energy eigenstates $|j\rangle$ (top to bottom: $j=0,...,4$) of the undriven bosonic Josephson junction (3) with fixed scaled interaction strength $N\kappa /\Omega =0.95$ vs particle number $N$.

Figure 2

(a) One Brillouin zone of exact quasienergies for the driven bosonic Josephson junction (4) with $N=100$ particles, scaled interaction strength $N\kappa /\Omega =0.95$, and scaled driving frequency $\omega /\Omega =1.62$, for low scaled driving amplitudes $2{\mu }_1/\omega$. The fan of almost equidistant lines is well described by the Mathieu approximation (8). (b) Part of the quasienergy spectrum for $N=500$, and higher driving amplitudes. Observe the scales!

Figure 3

Degree of coherence (6) for the near-resonant Floquet states with Mathieu quantum numbers $k=0,...,4$ (top to bottom) of the driven bosonic Josephson junction (4) with $N\kappa /\Omega =0.95$ kept fixed, $\omega /\Omega =1.62$, and $2{\mu }_1/\omega =0.3$, vs particle number $N$.

Figure 4

Maximum degree of coherence (6) of all $N$-particle Floquet states for $N\kappa /\Omega =0.95$ and $\omega /\Omega =1.62$. (a) $N=100$; the inset delimits the interval of driving strengths inspected in the following panel. (b) $N=500$; again the inset marks the interval investi-gated in the following panel. (c) $N=1000$. (d) $N=2000$. Observe the change of scale in comparison to (c), and the shift of the baseline.