An official website of the United States government
Abstract We study the trajectories of a semiclassical quantum particle under repeated indirect measurement by Kraus operators, in the setting of the quantized torus. In between measurements, the system evolves via either Hamiltonian propagators or metaplectic operators. We show in both cases the convergence in total variation of the quantum trajectory to its corresponding classical trajectory, as defined by the propagation of a semiclassical defect measure. This convergence holds up to the Ehrenfest time of the classical system, which is larger when the system is “less chaotic.” In addition, we present numerical simulations of these effects. In proving this result, we provide a characterization of a type of semi-classical defect measure we call uniform defect measures. We also prove derivative estimates of a function composed with a flow on the torus.
more »
« less
Quantum-classical correspondence of a system of interacting bosons in a triple-well potential
We study the quantum-classical correspondence of an experimentally accessible system of interacting bosons in a tilted triple-well potential. With the semiclassical analysis, we get a better understanding of the different phases of the quantum system and how they could be used for quantum information science. In the integrable limits, our analysis of the stationary points of the semiclassical Hamiltonian reveals critical points associated with second-order quantum phase transitions. In the nonintegrable domain, the system exhibits crossovers. Depending on the parameters and quantities, the quantum-classical correspondence holds for very few bosons. In some parameter regions, the ground state is robust (highly sensitive) to changes in the interaction strength (tilt amplitude), which may be of use for quantum information protocols (quantum sensing).
more »
« less
- Award ID(s):
- 1936006
- PAR ID:
- 10308882
- Date Published:
- Journal Name:
- Quantum
- Volume:
- 5
- ISSN:
- 2521-327X
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
-
-
We study the emergence of non-Gaussian quantum features in pulsed squeezed light generation with a mesoscopic number (i.e., dozens to hundreds) of pump photons. Due to the strong optical nonlinearities necessarily involved in this regime, squeezing occurs alongside significant pump depletion, compromising the predictions made by conventional semiclassical models for squeezing. Furthermore, nonlinear interactions among multiple frequency modes render the system dynamics exponentially intractable in naïve quantum models, requiring a more sophisticated modeling framework. To this end, we construct a nonlinear Gaussian approximation to the squeezing dynamics, defining a “Gaussian interaction frame” in which non-Gaussian quantum dynamics can be isolated and concisely described using a few dominant (i.e., principal) supermodes. Numerical simulations of our model reveal non-Gaussian distortions of squeezing in the mesoscopic regime, largely associated with signal-pump entanglement. We argue that state of the art in nonlinear nanophotonics is quickly approaching this regime, providing an all-optical platform for experimental studies of the semiclassical-to-quantum transition in a rich paradigm of coherent, multimode nonlinear dynamics. Mesoscopic pulsed squeezing, thus, provides an intriguing case study of the rapid rise in dynamic complexity associated with semiclassical-to-quantum crossover, which we view as a correlate of the emergence of new information processing capacities in the quantum regime.more » « less
-
It is possible that both the classical description of spacetime and the rules of quantum field theory emerge from a more-fundamental structure of physical law. Pregeometric frameworks transfer some of the puzzles of quantum gravity to a semiclassical arena where those puzzles pose less of a challenge. However, in order to provide a satisfactory description of quantum gravity, a semiclassical description must emerge and contain in its description a macroscopic spacetime geometry, dynamical matter, and a gravitational interaction consistent with general relativity at long distances. In this essay, we argue that a framework that includes a stochastic origin for quantum field theory can provide both the emergence of classical spacetime and a quantized gravitational interaction.more » « less
-
We study semiclassical perturbations of single-degree-of-freedom Hamiltonian systems possessing hyperbolic saddles with homoclinic orbits, and provide a sufficient condition for the separatrices to split, using a Melnikov-type approach. The semiclassical systems give approximations of the expectation values of the positions and momenta to the semiclassical Schrödinger equations with Gaussian wave packets as the initial conditions. The occurrence of separatrix splitting explains a mechanism for the existence of trajectories to cross the separatrices on the classical phase plane in the expectation value dynamics. Such separatrix splitting does not occur in standard systems of Hagedorn and Heller for the semiclassical Gaussian wave packet dynamics as well as in the classical systems. We illustrate our theory for the potential of a simple pendulum and give numerical computations for the stable and unstable manifolds in the semiclassical system as well as solutions crossing the separatrices.more » « less
-
A bstract The ODE/IM correspondence is an exact link between classical and quantum integrable models. The primary purpose of this work is to show that it remains valid after $$ \textrm{T}\overline{\textrm{T}} $$ T T ¯ perturbation on both sides of the correspondence. In particular, we prove that the deformed Lax pair of the sinh-Gordon model, obtained from the unperturbed one through a dynamical change of coordinates, leads to the same Burgers-type equation governing the quantum spectral flow induced by $$ \textrm{T}\overline{\textrm{T}} $$ T T ¯ . Our main conclusions have general validity, as the analysis may be easily adapted to all the known ODE/IM examples involving integrable quantum field theories.more » « less
- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.22331/q-2021-10-19-563
