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Physical Review A

Finite-dimensional coherent-state generation and quantum-optical nonlinear oscillator models

W. Leon-acuteski

Published May 1, 1997• 47 citations
Publisher

Abstract

We discuss a system comprising a cavity with a nonlinear medium of k-order and an external coherent field excitation. We assume that the cavity field was initially in vacuum state. We show that for the case of weak external field our system behaves similarly to one described in finite-dimensional Hilbert space. Moreover, we perform numerical calculations simulating the dynamics of our system and compare the results with those of analytical attempts.

DOI
10.1103/physreva.55.3874

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We discuss a system comprising a cavity with a nonlinear medium of k-order and an external coherent field excitation. We assume that the cavity field was initially in vacuum state. We show that for the case of weak external field our system behaves similarly to one described in finite-dimensional Hilbert space. Moreover, we perform numerical calculations simulating the dynamics of our system and compare the results with those of analytical attempts.
The authors begin by summarizing some schemes of generating finite-dimensional (FD) quantum-optical states. Although it is possible to generate n-photon Fock states and then to construct a desired state from these states, the focus of the chapter is on generation schemes that lead directly to the FD coherent states and FD squeezed vacuum. The method described is based on the quantum nonlinear oscillator evolution. The oscillator is assumed to be driven by external excitation. Depending on the character of the excitation, various FD states can be produced.
We studied a system that has two nonlinear oscillators with different frequencies. These oscillators are coupled via a nonlinear interaction. With the aim of excite the system, we used two external coherent fields. It follows from numerical simulation that evolution of the system which is likely to be a combination of Fock states. THerefore, the deliberated system behaves as so-called nonlinear quantum scissor. However, evolution of the system generates Bell-like states in some times with exact high probability. The system creates a truncation of optical states, which leads to obtain two-qubit states due to the nonlinear properties of oscillators and their interaction.
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 nnn-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 state 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.
We discuss a model of a cavity filled with a passive nonlinear ‚Kerr‘ medium and periodically kicked by a series of ultra-short laser pulses. The nonlinear medium is described by the (2q − 1)th nonlinearity X (2q−1). We find analytical formulas describing the field states inside the cavity. We show that such a system can produce, depending on the order of the nonlinearity, superpositions of several Fock states with the small photon numbers (0,1; 0,1,2; etc). In particular, the one-photon state can be approached during the evolution of the system with X (3) nonlinearity provided the cavity losses are negligible. The purity of states generated in this process, however, can be seriously degraded by the cavity damping. We perform numerical calculations to validate our analytical results.
A system comprising an anharmonic oscillator interacting with an external filed is discussed. The oscillator is assumed to be driven by a series of ultra-short external coherent pulses, and is initially in the vacuum state. It is shown that despite strong and permanent external excitations and lack of damping processes, for sufficiently short times between two subsequent pulses the system's evolution is restricted to a finite set of Fock n-photon states. Consequently, the mean energy of photons remains finite and the system evolves similarly to displaced Kerr states. The dynamics of the mean energy of photons is compared to that of its classical counterparts.