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Register a new userCavity-aided quantum parameter estimation in a bosonic double-well Josephson junction
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We describe an apparatus designed to make non-demolition measurements on a Bose-Einstein condensate (BEC) trapped in a double-well optical cavity. This apparatus contains, as well as the bosonic gas and the trap, an optical cavity. We show how the interaction between the light and the atoms, under appropriate conditions, can allow for a weakly disturbing yet highly precise measurement of the population imbalance between the two wells and its variance. We show that the setting is well suited for the implementation of quantum-limited estimation strategies for the inference of the key parameters defining the evolution of the atomic system and based on measurements performed on the cavity field. This would enable {it de facto} Hamiltonian diagnosis via a highly controllable quantum probe.
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We explore the interplay between tunneling and interatomic interactions in the dynamics of a bosonic Josephson junction. We tune the scattering length of an atomic $^{39}$K Bose-Einstein condensate confined in a double-well trap to investigate regimes inaccessible to other superconducting or superfluid systems. In the limit of small-amplitude oscillations, we study the transition from Rabi to plasma oscillations by crossing over from attractive to repulsive interatomic interactions. We observe a critical slowing down in the oscillation frequency by increasing the strength of an attractive interaction up to the point of a quantum phase transition. With sufficiently large initial oscillation amplitude and repulsive interactions the system enters the macroscopic quantum self-trapping regime, where we observe coherent undamped oscillations with a self-sustained average imbalance of the relative well population. The exquisite agreement between theory and experiments enables the observation of a broad range of many body coherent dynamical regimes driven by tunable tunneling energy, interactions and external forces, with applications spanning from atomtronics to quantum metrology.
We study the interplay between the dynamics of a Bose-Einstein condensate in a double-well potential and that of an optical cavity mode. The cavity field is superimposed to the double-well potential and affects the atomic tunneling processes. The cavity field is driven by a laser red detuned from the bare cavity resonance; the dynamically changing spatial distribution of the atoms can shift the cavity in and out of resonance. At resonance the photon number is hugely enhanced and the atomic tunneling becomes amplified. The Josephson junction equations are revisited and the phase diagram is calculated. We find new solutions with finite imbalance and at the same time a lack of self-trapping solutions due to the emergence of a new separatrix resulting from enhanced tunneling.
We study the influence of photons on the dynamics and the ground state of the atoms in a Bosonic Josephson junction inside an optical resonator. The system is engineered in such a way that the atomic tunneling can be tuned by changing the number of photons in the cavity. In this setup the cavity photons are a new means of control, which can be utilized both in inducing self-trapping solutions and in driving the crossover of the ground state from an atomic coherent state to a Schrodingers cat state. This is achieved, for suitable setup configurations, with interatomic interactions weaker than those required in the absence of cavity. This is corroborated by the study of the entanglement entropy. In the presence of a laser, this quantum indicator attains its maximum value (which marks the formation of the cat-like state and, at a semiclassical level, the onset of self-trapping) for attractions smaller than those of the bare junction.
We calculate the first two moments and full probability distribution of the work performed on a system of bosonic particles in a two-mode Bose-Hubbard Hamiltonian when the self-interaction term is varied instantaneously or with a finite-time ramp. In the instantaneous case, we show how the irreversible work scales differently depending on whether the system is driven to the Josephson or Fock regime of the bosonic Josephson junction. In the finite-time case, we use optimal control techniques to substantially decrease the irreversible work to negligible values. Our analysis can be implemented in present-day experiments with ultracold atoms and we show how to relate the work statistics to that of the population imbalance of the two modes.
In this paper we consider a bosonic Josephson junction described by a two-mode Bose-Hubbard model, and we thoroughly analyze a quantum phase transition occurring in the system in the limit of infinite bosonic population. We discuss the relation between this quantum phase transition and the dynamical bifurcation occurring in the spectrum of the Discrete Self Trapping equations describing the system at the semiclassical level. In particular, we identify five regimes depending on the strength of the effective interaction among bosons, and study the finite-size effects arising from the finiteness of the bosonic population. We devote a special attention to the critical regime which reduces to the dynamical bifurcation point in the thermodynamic limit of infinite bosonic population. Specifically, we highlight an anomalous scaling in the population imbalance between the two wells of the trapping potential, as well as in two quantities borrowed from Quantum Information Theory, i.e. the entropy of entanglement and the ground-state fidelity. Our analysis is not limited to the zero temperature case, but considers thermal effects as well.
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