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Chinese Physics B

Evolution law of a negative binomial state in an amplitude dissipative channel

Feng Chen, Hong-Yi Fan

Published Mar 1, 2014• 9 citations
Publisher

Abstract

For the first time we derive the evolution law of the negative binomial state in an amplitude dissipative channel with a damping constant κ. We find that after passing through the channel, the final state is still a negative binomial state, however the parameter γ evolves into γ', where γ = γ/(e−2κt (1 − γ) + γ). The decay law of the average photon number is also obtained.

DOI
10.1088/1674-1056/23/3/030304

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For the first time we derive the evolution law of the negative binomial state in an amplitude dissipative channel with a damping constant κ. We find that after passing through the channel, the final state is still a negative binomial state, however the parameter γ evolves into γ', where γ = γ/(e−2κt (1 − γ) + γ). The decay law of the average photon number is also obtained.
We show that passing through the amplitude dissipative channel the initial pure number state density operator is evolved into the density operator of binomial distribution (a mixed state), and the binomial distribution parameter is just equal to e −2 kt , where k is the dissipative parameter of the channel. We solve the corresponding master equation to obtain the operator-sum representation of the density operator by virtue of the entangled state representation, which seems to be a convenient approach.
We propose a new optical field and show that such an optical field can be generated as an output of a displaced Fock state in an amplitude dissipative channel.We derive new generating function formulas and binomial formula involving twovariable Hermite polynomials to reach this result.The photon number average in this new optical field is m+|α|2e-2κt,which indicates that controlling the photon number can be realized by adjusting the value of m or|α|2orκ.The time evolution law of displaced Fock state in a thermo reservoir is thus revealed.
We propose a new optical field and show that such an optical field can be generated as an output of a displaced Fock state in an amplitude dissipative channel. We derive new generating function formulas and binomial formula involving two-variable Hermite polynomials to reach this result. The photon number average in this new optical field is which indicates that controlling the photon number can be realized by adjusting the value of m or |α| 2 or κ . The time evolution law of displaced Fock state in a thermo reservoir is thus revealed.