Abstract
The ability to cool quantum gases into the quantum degenerate realm has opened up possibilities for an extreme level of quantum-state control. In this paper, we investigate one such control protocol that demonstrates the resonant amplification of quasimomentum pairs from a Bose–Einstein condensate by the periodic modulation of the two-body s-wave scattering length. This shows a capability to selectively amplify quantum fluctuations with a predetermined momentum, where the momentum value can be spectroscopically tuned. A classical external field that excites pairs of particles with the same energy but opposite momenta is reminiscent of the coherently-driven nonlinearity in a parametric amplifier crystal in nonlinear optics. For this reason, it may be anticipated that the evolution will generate a ‘squeezed’ matter-wave state in the quasiparticle mode on resonance with the modulation frequency. Our model and analysis is motivated by a recent experiment by Clark et al that observed a time-of-flight pattern similar to an exploding firework (Clark et al 2017 Nature 551 356–9). Since the drive is a highly coherent process, we interpret the observed firework patterns as arising from a monotonic growth in the two-body correlation amplitude, so that the jets should contain correlated atom pairs with nearly equal and opposite momenta. We propose a potential future experiment based on applying Ramsey interferometry to experimentally probe these pair correlations.
Highlights
The ability to tune the two-body scattering length in a Bose-Einstein Condensate (BEC) by varying the magnitude of a magnetic field in the vicinity of a Feshbach resonance has been employed in a number of seminal experiments that aim to investigate controlled non-equilibrium quantum dynamics
The dynamics of the system under this modulation is interesting to consider because the oscillating external field will inject energy into the system, and this will result in exciting atoms from the ground state into higher quasiparticle levels
We have developed a description of a condensate and non-condensate system starting from the many-body field theory Hamiltonian and deriving the evolution equations for the condensate, normal density and anomalous density
Summary
The ability to tune the two-body scattering length in a Bose-Einstein Condensate (BEC) by varying the magnitude of a magnetic field in the vicinity of a Feshbach resonance has been employed in a number of seminal experiments that aim to investigate controlled non-equilibrium quantum dynamics. Bose ‘firework’ experiments [1] have observed pairs of high momentum atoms emitted as jets from a condensate driven by a periodic modulation of the two-body s-wave scattering length These experiments demonstrated a protocol for resonantly amplifying quantum fluctuations with well-controlled momenta when starting from a stationary BEC. In the case of a dilute quantum gas, the Gross-Pitaevskii equation (GPE) provides an accurate description of the equilibrium and time-dependent behavior of the BEC In this framework, the interacting condensate is completely described by a mean-field superfluid order parameter. Neglecting collisions is a good approximation for a dilute gas at low temperature, but implicitly requires us to limit our discussion to the regime in which the time-scale between consecutive two-body collision events greatly exceeds the time-scale of the quantum dynamics that we investigate All this has to be implemented in multiple dimensions in order to provide a useful comparison with experimental observations.
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