Classical limit of bosons in phase space

A. O. Bolivar

Pavel Cejnar

We discuss features of quantum phase transitions affecting collective dynamics of many-body systems. Due to a finite number of collective degrees of freedom, the infinite-size limit of the corresponding models coincides with the classical limit and quantum critical phenomena for both the ground and excited states are determined by the structure of the classical phase space. An example of an excited-state phase transition for the interacting boson model in its SU(3) limit is presented.

A.E.L. Dieperink, Olaf Scholten, FRANCESCO IACHELLO

Heliques Mesquita Frazao

In this work, we study an effective three-mode Hamiltonian describing interacting bosons. These bosons can be considered as exciton-polaritons in a semiconductor microcavity at the magic angle or cold atoms optically trapped in a triple-well potential with a population imbalance conservation. We observe that the quantum properties of the spectrum characterize a quantum phase transition. We realize a thermodynamic limit of the Hamiltonian and we study the classical properties of the phase space. We observe a close analogy between quantum and classical properties: an inflection point (a level approximation) in spectrum corresponds to a separatrix (a trajectory that separates librations and rotations) in phase space. This analogy allows us to characterize the system phases, the order of the transition, and also to construct a phase diagram.

Stanisław Świerczewski, Wouter Verstraelen, Piotr Deuar +4 more

Quantum optical neural networks (QONNs) enable information processing beyond classical limits by exploiting the advantages of classical and quantum optics. However, simulation of large-scale bosonic lattices remains a significant challenge due to the exponential growth of the Hilbert space required to describe a quantum network accurately. Consequently, previous theoretical studies have been limited to small-scale systems, leaving the behaviour of multimode QONNs largely unexplored. This work presents an efficient computational framework based on the phase-space positive-P method for simulating bosonic neuromorphic systems. This approach provides a view to previously inaccessible regimes, allowing the validation of large-scale bosonic networks in various quantum machine learning tasks such as quantum state classification and quantum state feature prediction. Our results show that the performance of a large quantum reservoir does not improve monotonously with the number of bosonic modes, instead following a complex dependence driven by the interplay of nonlinearity, reservoir size, and the average occupation of the input mode. These findings are essential for designing and optimising optical bosonic reservoirs for future quantum neuromorphic computing devices.

Yoel Tikochinsky, Dror Shalitin