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Chinese Physics B

Dissipation of a two-mode squeezed vacuum state in the single-mode amplitude damping channel

Nanrun Zhou, Liyun Hu, Hong-Yi Fan

Published Dec 1, 2011• 11 citations
Publisher

Abstract

We explore how a two-mode squeezed vacuum state sechθe a † b † tanhθ |00〉 evolves when it undergoes a single-mode amplitude dissipative channel with rate of decay κ. We find that in this process not only the squeezing parameter decreases, tanhθ → e −κt tanhθ, but also the second-mode vacuum state evolves into a chaotic state exp{ b † b ln[(1 − e −2κt )tanh 2 θ]}. The outcome state is no more a pure state, but an entangled mixed state.

DOI
10.1088/1674-1056/20/12/120301

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We explore how a two-mode squeezed vacuum state sechθe a † b † tanhθ |00〉 evolves when it undergoes a single-mode amplitude dissipative channel with rate of decay κ. We find that in this process not only the squeezing parameter decreases, tanhθ → e −κt tanhθ, but also the second-mode vacuum state evolves into a chaotic state exp{ b † b ln[(1 − e −2κt )tanh 2 θ]}. The outcome state is no more a pure state, but an entangled mixed state.
Extending the recent work completed by Fan et al. [ Front. Phys. 9(1), 74 (2014)] to a two-mode case, we investigate how a two-mode squeezed vacuum evolves when it undergoes a two-mode amplitude dissipative channel, with the same decay rate κ, using the continuous-variable entangled state approach. Our analytical results show that the initial pure-squeezed vacuum state evolves into a definite mixed state with entanglement and squeezing, decaying over time as a result of amplitude decay. We also investigate the time evolutions of the photon number distribution, the Wigner function, and the optical tomogram in this channel. Our results indicate that the evolved photon number distribution is related to Jacobi polynomials, the Wigner function has a standard Gaussian distribution (corresponding to the vacuum) at long periods, losing its nonclassicality due to amplitude decay, and a larger squeezing leads to a longer decay time.
For the first time we derive the dissipating result of an initial two-mode squeezed pure vacuum state passing through a two-mode amplitude dissipative channel described by the direct product of two independent single-mode master equations. Although these two master equations do not mix the two modes (there is no coupling between them), since the two-mode squeezed state is simultaneously an entangled state, the final state which emerges from passing this channel is a two-mode mixed density operator. The compact expression of the outcoming state is obtained, which manifestly shows that as time evolves, the squeezing effect decreases.
Using the way of deriving infinitive sum representation of density operator as a solution to the master equation describing the amplitude dissipative channel by virtue of the entangled state representation, we show manifestly how the initial density operator of a single-mode squeezed vacuum state evolves into a definite mixed state which turns out to be a squeezed chaotic state with decreasing-squeezing and decoherence. We investigate average photon number, photon statistics distributions for this mixed state.
In this paper, we investigate how a kind of non-Gaussian states (l-photon excited thermo vacuum state [Formula: see text]) evolves in a single-mode damping channel. We find that it evolves into a Laguerre-polynomial-weighted real–fictitious squeezed thermo vacuum state, which exhibits strong decoherence and its original nonclassicality fades. In particular, when l = 0, in this damping process the thermo squeezing effect decreases while the fictitious-mode vacuum becomes chaotic. In overcoming the difficulty of calculation, we employ the summation method within ordered product of operators, a new generating function formula about two-variable Hermite polynomials is derived.