Finite-dimensional states and entanglement generation for a nonlinear coupler

Abstract

We discuss a system comprising two nonlinear (Kerr-like) oscillators coupled mutually by a nonlinear interaction. The system is excited by an external coherent field that is resonant to the frequency of one of the oscillators. We show that the coupler evolution can be closed within a finite set of n-photon states, analogously as in the nonlinear quantum scissors model. Moreover, for this type of evolution our system can be treated as a Bell-like states generator. Thanks to the nonlinear nature of both: oscillators and their internal coupling, these states can be generated even if the system exhibits its energy dissipating nature, contrary to systems with linear couplings.

Nonlinear coupler operating on Werner-like states—entanglement creation, its enhancement, and preservation

“…The systems involving Kerr-like quantum oscillators can also be applied as sources of quantum states defined in finite-dimensional Hilbert space, and are referred to as nonlinear quantum scissors (NQS). Applying such systems one can generate one-mode [10][11][12][13][14], two-mode [15,16], or three-mode truncated states [17] (for review of problems related to NQS see [18][19][20] and the references quoted therein. From other side, one should mention that Werner or Werner-like states that we shall discuss here, are widely applied in various quantum information theory models.…”

“…We will show that our system, interacting with external bath, behaves as two-qutrit one. Although the * Corresponding author: w.leonski@if.uz.zgora.pl evolution of the entanglement in two-qubit, qubit-qutrit or two-qutrit systems, interacting with various types of reservoirs, was already discussed in the previous papers (for instance, see [16,[24][25][26] and the references quoted therein) but was considered only for cases of initial pure states: Fock or maximally entangled states. One of the purposes of this paper is to show that effective state truncation and entanglement creation is also possible for other initial states: mixed states and Werner-like ones (which are mixtures of Bell and mixed states).…”

General linear-optical quantum state generation scheme: Applications to maximally path-entangled states

“…One approach to the problem is to make use of an optical nonlinearity. However, due to the relatively small average number of photons involved, the overall nonlinear effect is extremely weak and typically of little practical use [8,9,10]. An alternative way to enable an effective photon-photon interaction is to use ancilla modes and projective measurements [2,3].…”

Kerr nonlinear coupler and entanglement induced by broadband laser light

“…It is shown that the coupler evolution governed by the same effective Hamiltonians as usual optical Kerr couplers (discussed for instance in [4]) can be closed within a finite set of n-photon states. After "truncation" of the wave function describing the system, the coupler can be treated as two-qubit and treated as a Bell-like state generator that can create maximally entangled states even if the system exhibits its energy dissipating nature [5]. The system behaves similar to nonlinear quantum scissors and maximally entangled Bell states can be generated with high efficiency [6].…”