Abstract
We investigate the behavior of a one-dimensional Bose-Hubbard gas in both a ring and a hard-wall box, whose kinetic energy is made to oscillate with zero time-average, which suppresses first-order particle hopping. For intermediate and large driving amplitudes the system in the ring has similarities to the Richardson model, but with a peculiar type of pairing and an attractive interaction in momentum space. This analogy permits an understanding of some key features of the interacting boson problem. The ground state is a macroscopic quantum superposition, or cat state, of two many-body states collectively occupying opposite momentum eigenstates. Interactions give rise to a reduction (or modified depletion) cloud that is common to both macroscopically distinct states. Symmetry arguments permit a precise identification of the two orthonormal macroscopic many-body branches which combine to yield the ground state. In the ring, the system is sensitive to variations of the effective flux but in such a way that the macroscopic superposition is preserved. We discuss other physical aspects that contribute to protect the cat-like nature of the ground state.
Highlights
The existence of macroscopic quantum superposition (MQS) states, or cat states, has long been one of the most counterintuitive predictions of quantum mechanics [1], as it is at odds with our daily perception of reality, where such states are not observed
Numerical inspection shows that the main difference between the ground and the first excited states is their behavior under time reversal, i.e., the transformation that changes the sign of all momenta (k → −k)
In this paper we have investigated a novel type of Schrödinger cat state whose main characteristic is its unusual resilience to collapse into one of its branches
Summary
The existence of macroscopic quantum superposition (MQS) states, or cat states, has long been one of the most counterintuitive predictions of quantum mechanics [1], as it is at odds with our daily perception of reality, where such states are not observed. The collapse of the Schrödinger cat state into one of its branches prevents us from directly observing coherent superpositions of macroscopically distinct states. This collapse is understood to be induced by the decohering effect of a dissipative environment which, in particular, can be a measuring apparatus [2,3,4,5]. The ground state is a cat state involving two branches in which two different nonzero momentum states are macroscopically occupied In both the ring and the hard-wall cases, the system’s resilience against collapse shows important differences as compared with other setups hosting catlike states. The paper is complemented by Appendices dealing with a variational calculation and a cat measure estimate
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