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Journal of Modern Optics

Finite energy states generation by periodically pulsed nonlinear oscillator

W. Leoński

Published Apr 1, 2001• 3 citations
Publisher

Abstract

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.

DOI
10.1080/09500340010011754

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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.
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.
We consider quantum dynamics of a parametrically driven anharmonic oscillator (PDAO) at a few-photon level. In this scheme the oscillatory mode is excited through the degenerate down-conversion process. This scheme could be experimentally realized in superconducting solid-state devices based on the nonlinearity of the Josephson junction or in cooled nano-mechanical oscillators. We investigate PDAO in the strong quantum regime that means strong Kerr-nonlinearity of the mode with respect to the mode’s dissipation for two cases of excitations: by a monochromatic driving field or by a train of Gaussian pulses. We demonstrate production of the nonclassical oscillatory states with two-fold symmetry in phase-space which are approximately close to the lower pure Fock states. Production of the superposition of the Fock states for time-intervals exceeding the characteristic time of decoherence and dissipation is also shown.