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International Journal of Modern Physics Conference Series

PRODUCTION OF FOCK STATES IN NONLINEAR OSCILLATOR DUE TO PULSED EXCITATION

T. V. Gevorgyan, A. R. Shahinyan, Gagik Yu. Kryuchkyan

Published Jan 1, 2012• 0 citations
Publisher

Abstract

The Fock states are usually generated by using interaction of oscillatory mode with atomic systems driven by a coherent field. We demonstrate that production of Fock states is also realized in the specific operational regimes of a single nonlinear oscillator without any interactions with atomic systems due to its excitation by a series of short Gaussian laser pulses. These results are demonstrated for the case of the strong Kerr nonlinearity and in the presence of dissipation and decoherence.

DOI
10.1142/s2010194512006927

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The Fock states are usually generated by using interaction of oscillatory mode with atomic systems driven by a coherent field. We demonstrate that production of Fock states is also realized in the specific operational regimes of a single nonlinear oscillator without any interactions with atomic systems due to its excitation by a series of short Gaussian laser pulses. These results are demonstrated for the case of the strong Kerr nonlinearity and in the presence of dissipation and decoherence.
We demonstrate a quantum regime of dissipative nonlinear oscillators where the creation of Fock states as well as the superpositions of Fock states are realized for time intervals exceeding the characteristic decoherence time. The preparation of quantum states is conditioned by strong Kerr nonlinearity as well as by excitation of resolved lower oscillatory energy levels with a specific train of Gaussian pulses. This provides practical signatures to look for in experiments with cooled nonlinear oscillators.
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.
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 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.
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