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Nonlinear Dynamics

Enhancement of the entanglement generation via randomly perturbed series of external pulses in a nonlinear Bose–Hubbard dimer

Joanna K. Kalaga, A. Kowalewska-Kudłaszyk, M.W. Jarosik, Radosław Szczȩśniak, W. Leoński

Published Jun 27, 2019• 9 citations
Publisher

Abstract

We discuss a model of a short Bose–Hubbard dimer involving two anharmonic quantum oscillators mutually coupled with the use of the linear interaction and additionally driven by a series of ultra-short external pulses. We show that under some conditions the system behaves as a two-qubit one, and contrary to its continuously driven counterpart can be a source of maximally entangled states (MES). We discuss the cases when the system is excited only in one mode and in both ones, and additionally when the cross-Kerr-type interaction is present or omitted. We show that the generation of maximally (or almost maximally) entangled states depends on the time of free evolution of oscillators and hence, the proper steering of the changes of the time between subsequent pulses can increase the effectiveness of MES generation. Moreover, we show the influence of the timing between two series of pulses (corresponding to the two modes) on such a process. What is relevant, thanks to the presence of additional randomness in the timings, the states with stronger entanglement can be achieved than for the situation when the time between consecutive pulses remains ideally fixed.

DOI
10.1007/s11071-019-05084-5

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We discuss a model of a short Bose–Hubbard dimer involving two anharmonic quantum oscillators mutually coupled with the use of the linear interaction and additionally driven by a series of ultra-short external pulses. We show that under some conditions the system behaves as a two-qubit one, and contrary to its continuously driven counterpart can be a source of maximally entangled states (MES). We discuss the cases when the system is excited only in one mode and in both ones, and additionally when the cross-Kerr-type interaction is present or omitted. We show that the generation of maximally (or almost maximally) entangled states depends on the time of free evolution of oscillators and hence, the proper steering of the changes of the time between subsequent pulses can increase the effectiveness of MES generation. Moreover, we show the influence of the timing between two series of pulses (corresponding to the two modes) on such a process. What is relevant, thanks to the presence of additional randomness in the timings, the states with stronger entanglement can be achieved than for the situation when the time between consecutive pulses remains ideally fixed.
A system of two coupled quantum oscillators in the Bose–Hubbard model is discussed as a source of maximally entangled states obtained by ultrashort coherent pulses. Both oscillators are externally driven, and by appropriate relations between the frequencies, we can manipulate the degree of entanglement in bosonic modes. Created entanglement between two subsystems can be controlled and depends strictly on the number of pulses applied to one of the coupler’s parts during a unitary evolution of the other. It is shown that the creation of maximally entangled states is possible, especially for cases when applying other types of excitations (continuous driving or simultaneous excitations) leads to a very weak entanglement of the coupled bosonic system.
We consider a nonlinear coupler with two Kerr-like oscillators mutually coupled by continuous linear interaction and excited by a series of ultrashort external pulses. We show that the system behaves like nonlinear quantum scissors . It evolves in such a way that it can be treated as a qubit–qubit system. We derive analytic formulas for the probabilities of the states involved in the system's evolution and show that they differ from those already discussed in the literature and corresponding to the continuously excited models. Moreover, for the model discussed here, maximally entangled Bell states can be generated with high efficiency.
We study a model with two nonlinear oscillators (Kerr-like nonlinear coupler) pumped by two external coherent fields as a nonlinear quantum scissor (NQS). Using the numerical simulation method introduced before for quantum state engineering in NQS of such type, we obtain the wave function describing the evolution of the system as a combination of n-photon states. Considered NQS generates a truncation of optical states that leads to achieve two-qubit states due to the nonlinear properties of oscillators and their interaction. In particular, evolution of the system generates maximally entangled states as so-called Bell-like states. We will show that a proper choice of initial conditions for such evolution implies the increase of efficiency of entanglement creation process. We consider our model for both damping and without damping cases.
We discuss a model of two nonlinear Kerr-like oscillators, mutually coupled and excited by parametric process. We show that the system’s evolution, starting from Werner-like states, remains closed within a small set of two-mode n-photon states and that a pure two-qubit entangled state can be generated. For some initial Werner-like states, delayed entanglement generation can be observed. We investigate the influence of two damping mechanisms on the system’s evolution. We show that, for both cases, entanglement can survive despite the presence of damping, and that the effects of sudden entanglement death and its rebirth can appear in the system.
We consider time-evolution of the disentanglement process of once generated entangled qubit pair as a result of the phase variation of the pumping field. As a source of maximally entangled states we use the nonlinear coupler (two oscillators with Kerr-like nonlinearities) with nonlinear internal interactions. The coupler prepared in a maximally entangled state interacts afterwards with external reservoir of thermal character and pumping field as well. We show that the fact of the coupling with additional state (which can create additional entanglement with one of the 2-qubit system's previously entangled states) is an origin of interesting entanglement decay behaviour. We can observe shortening of both: entanglement death-time and entanglement birth caused by changing the phase of an external driving field.