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Tuneable interacting bosons for relativistic and quantum information processing

Chester Moore, David Edward Bruschi

Published Jan 8, 2016• 2 citations
OpenAlex

Abstract

We study the full time evolution of a system of two modes of a bosonic quantum field that interact through quadratic hamiltonians. We specialise to a time dependent two-mode squeezing Hamiltonian where the coupling is switched on and off smoothly. We find the analytical solutions to the time evolution after the interaction is turned off, which apply to arbitrary coupling functions. We investigate the final state of the system and compute all physically relevant quantities, such as average particle number, entanglement and change in energy. Our techniques can be applied to a wide range of scenarios, which include implementations of time dependent two-mode squeezing, coupled harmonic oscillators, harmonic oscillators coupled to light. Furthermore, these techniques can be extended to more complicated time-dependent quadratic Hamiltonians. We briefly discuss possible applications within the area of relativistic and quantum information.

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We study the full time evolution of a system of two modes of a bosonic quantum field that interact through quadratic hamiltonians. We specialise to a time dependent two-mode squeezing Hamiltonian where the coupling is switched on and off smoothly. We find the analytical solutions to the time evolution after the interaction is turned off, which apply to arbitrary coupling functions. We investigate the final state of the system and compute all physically relevant quantities, such as average particle number, entanglement and change in energy. Our techniques can be applied to a wide range of scenarios, which include implementations of time dependent two-mode squeezing, coupled harmonic oscillators, harmonic oscillators coupled to light. Furthermore, these techniques can be extended to more complicated time-dependent quadratic Hamiltonians. We briefly discuss possible applications within the area of relativistic and quantum information.
We study the time evolution of an ideal system composed of two harmonic oscillators coupled through a quadratic Hamiltonian with arbitrary interaction strength. We solve its dynamics analytically by employing tools from symplectic geometry. In particular, we use this result to completely characterize the dynamics of the two oscillators interacting in the ultrastrong-coupling regime with additional single-mode squeezing on both oscillators, as well as higher-order terms. Furthermore, we compute quantities of interest, such as the average number of excitations and the correlations that are established between the two subsystems due to the evolution. We find that this model predicts a second-order phase transition and we compute the critical exponents and the critical value. We also provide an exact decoupling of the time evolution in terms of simple quantum optical operations, which can be used for practical implementations and studies. Finally, we show how our techniques can be extended to include more oscillators and higher-order interactions.
The techniques employed to solve the interaction of a detector and a quantum field typically require perturbation methods. We introduce mathematical techniques to solve the time evolution of an arbitrary number of detectors interacting with a quantum field. Our techniques apply to harmonic oscillator detectors and can be generalized to treat detectors modeled by quantum fields. Since the interaction Hamiltonian we introduce is quadratic in creation and annihilation operators, we are able to draw from continuous variable techniques commonly employed in quantum optics.
We study the full time evolution of one- and two-mode bosonic quantum systems that interact through single- and two-mode squeezing Hamiltonians. We establish that the single- and two-mode cases are formally equivalent, leading to the same differential equations encoding the full time evolution. These differential equations can be easily employed in any application. We analytically predict a dramatic transition in the population of the modes when the coupling takes a specific critical value, leading to exponential growth of the excitation population. We discuss the validity, scope and generality of our results.
Quantum harmonic oscillators model a wide variety of phenomena ranging from electromagnetic fields to vibrations of atoms in molecules. Their excitations can be represented by bosons such as photons, single particles of light, or phonons, the quanta of vibrational energy. Linear interactions that only create and annihilate single bosons can generate coherent states of light or motion. Introducing nth-order nonlinear interactions, that instead involve n bosons, leads to increasingly complex quantum behaviour. For example, second-order interactions enable squeezing, used to enhance the precision of measurements beyond classical limits, while higher-order interactions create non-Gaussian states essential for continuous-variable quantum computation. However, generating nonlinear interactions is challenging, typically requiring higher-order derivatives of the driving field or specialized hardware. Hybrid systems, where linear interactions couple an oscillator to an additional spin, offer a solution and are readily available across many platforms. Here, using the spin of a single trapped ion coupled to its motion, we employ two linear interactions to demonstrate up to fourth-order bosonic interactions; we focus on generalised squeezing interactions and demonstrate squeezing, trisqueezing, and quadsqueezing. We characterise these interactions, including their spin dependence, and reconstruct the Wigner function of the resulting states. We also discuss the scaling of the interaction strength, where we drive the quadsqueezing interaction more than 100 times faster than using conventional techniques. Our method presents no fundamental limit in the interaction order n and applies to any platform supporting spin-dependent linear interactions. Strong higher-order nonlinear interactions unlock the study of fundamental quantum optics, quantum simulation, and computation in a hitherto unexplored regime.
We study the time evolution of bosonic systems where multiple driven bosonic modes of light interact with multiple mechanical resonators through arbitrary, time-dependent, optomechanicallike interactions. We find the analytical expression for the full time evolution of the system and compute the expectation value of relevant quantities of interest. Among the most interesting ones, we are able to compute the first-order quantum bipartite coherence between pairs of subsystems, and the analytical expression for the mixedness induced by the nonlinear interaction in the reduced state of the mechanical oscillators. Finally, we also compare our results with a linearized version of the system, and we find a regime where there are qualitative and quantitative differences in the behavior of some measurable quantities. Our results can, therefore, be used to describe the full time-evolution of the system to characterize its nonlinear character and explore the validity of the linearization approach.