Quantum signatures and semiclassical limitations in the transmission of Fock states

Abstract

Transmission through potential barriers is a fundamental problem in quantum mechanics. While semiclassical methods can approximate certain aspects of transmission, they fail to capture the intrinsically quantum interference associated with Wigner-function negativity. We numerically study the transmission of displaced Fock states through an inverted-oscillator barrier, with and without a Kerr nonlinearity that offers a potential route to experimental realization. These states allow only an approximate classical description, since their characteristic Wigner-function negativity is absent in phase space. The semiclassical simulation reproduces the overall transmission but deviate from exact results and fail to capture short-time plateaus that arise when regions of Wigner-function negativity cross the barrier. With the Kerr nonlinearity, reflections from nonlinear boundaries drive interference into classically forbidden regions, an effect that is inaccessible to semiclassical approaches. We find that these interference effects do not alter the maximum transmission probability, which is bounded by the initial positive-energy fraction and therefore already encoded in the phase-space structure of the Fock states. Because Fock states cannot be faithfully represented within classical phase space, the transmission through a barrier reveals fundamental limitations of semiclassical approaches.

References in corpus (26)

• Reconstruction of non-classical cavity field states with snapshots of their decoherence
• Quantum information with Gaussian states
• Many-Body Quantum Spin Dynamics with Monte Carlo Trajectories on a Discrete Phase Space
• Switching via quantum activation: A parametrically modulated oscillator
• Effect of higher-order nonlinearities on amplification and squeezing in Josephson parametric amplifiers
• Tunneling dynamics of few bosons in a double well
• Revealing nonclassicality beyond Gaussian states via a single marginal distribution
• Spectral kissing and its dynamical consequences in the squeeze-driven Kerr oscillator
• Semi-classical formula for quantum tunneling in asymmetric double-well potentials
• Propagating Wigner-Negative States Generated from the Steady-State Emission of a Superconducting Qubit
• Non-Gaussian pure states and positive Wigner functions
• Avoided crossings and dynamical tunneling close to excited-state quantum phase transitions
• Quantum tunneling and level crossings in the squeeze-driven Kerr oscillator
• Quantification of Wigner Negativity Remotely Generated via Einstein-Podolsky-Rosen Steering
• Quantum Phase Transition in Finite-Size Lipkin-Meshkov-Glick Model
• Localization or tunneling in asymmetric double-well potentials
• Symmetries of the squeeze-driven Kerr oscillator
• Effective quantum tunneling from semiclassical momentous approach
• Quantum inverted harmonic potential
• Husimi dynamics generated by non-Hermitian Hamiltonians
• Spontaneous emission from a two--level atom tunneling in a double--well potential
• Phase-space consideration on barrier transmission in a time-dependent variational approach with superposed wave packets
• Quantum instability and Ehrenfest time for an inverted harmonic oscillator
• Many-body tunneling in a double-well potential
• Phase transitions, symmetries, and tunneling in Kerr parametric oscillators
• A numerical study of the Bose-Einstein condensates in a double-well trap using finite differences