A reappraisal of two-mode squeezing and intermode coupling
30 Apr 2000-Modern Physics Letters A (World Scientific Publishing Company)-Vol. 15, Iss: 13, pp 825-831
TL;DR: In this article, the authors derived the result that the two-mode squeezed state is factorizable in terms of the component single modes of a pair of coupled oscillators and considered the effects of a sudden switching-on of the intermode coupling for these quadrature modes.
Abstract: We study two-mode squeezing in the framework of generalized quantum condition and derive pedagogically the result that the two-mode squeezed state is factorizable in terms of the component single modes. We also examine the related problem of two-mode squeezing in the system of a pair of coupled oscillators and consider the effects of a sudden switching-on of the intermode coupling for these quadrature modes.
Citations
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TL;DR: This review is intended for readers who want to have a quick understanding on the theoretical underpinnings of coherent states and squeezed states which are conventionally generated from the prototype harmonic oscillator but not always restricting to it.
Abstract: This review is intended for readers who want to have a quick understanding on the theoretical underpinnings of coherent states and squeezed states which are conventionally generated from the protot...
11 citations
Cites background or methods from "A reappraisal of two-mode squeezing..."
...2 tanhΘ|0,0i (9.11) is also expressible as |0Θi = e−lncoshΘe i 2 (Λ+†2−Λ−†2)tanhΘ|0,0i (9.12) The above result makes it transparent that squeezing for two-mode quantum systems [64] can be interpreted [69,70] as the direct product of two single-mode squeezed states. Even squeezed multi-mode wave function can be shown to arise [125,126] from the single-mode squeezed state for the normal modes. 10 SQMapproa...
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...emperature. Two-mode squeezing can be looked upon as some kind of thermofield state [66,67] whose evolution is through the Wigner function [68]. It is known [69] that multi-mode squeezing could result [70] from the product of component single-modes, each of which is generated from the ground Fock space. This 3The term squeezing was coined by Hollenhorst [43]. 4 framework proves rather convenient to han...
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...mine the possibility of relating two-mode squeezing as a system of a pair of coupled oscillators. To begin with let us combine the two commutations given by (8.2) into a generalized quantum condition [70]. For this we make use of the replacements p1 → −i ∂ ∂x1 −ig(x2) (9.1) p2 → i ∂ ∂x2 −if(x1) (9.2) implying that the two-mode squeezed state wave function ψΘ(x1,x2) = hx1,x2|0Θi would obey the different...
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...by a direct application of a unitary operator on the ground Fock state, its generator being an element of the Cartan subalgebra of Sp(2n;R). However, in this review, we will adopt a different strategy [70] to establish a similar idea by concentrating on the two-mode squeezing focusing on different aspects of its theoretical status. Two-mode squeezing has also been interpreted as a system of a pair of co...
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TL;DR: In this article, the authors derived nonlinear squeezed states and the multiplication rule of nonlinear squeezing operators using nonlinear coherent state representation and the technique of integral within an ordered product of operators.
Abstract: Using the nonlinear coherent state representation we derive nonlinear squeezed states and the multiplication rule of nonlinear squeezing operators. We find that the symplectic matrices multiplication rule in nonlinear coherent state projection operator representation maps into the multiplication rule of successive nonlinear squeezing operators. The technique of integral within an ordered product of operators plays an essential role in deriving the multiplication rule.
2 citations
TL;DR: In this paper, the theoretical underpinnings of coherent states and squeezed states are discussed and a review is given for readers who want to have a quick understanding on the theoretical foundations of coherent state and squeezed state.
Abstract: This review is intended for readers who want to have a quick understanding on the theoretical underpinnings of coherent states and squeezed states which are conventionally generated from the prototype harmonic oscillator but not always restricting to it. Noting that the treatments of building up such states have a long history, we collected the important ingredients and reproduced them from a fresh perspective but refrained from delving into detailed derivation of each topic. By no means we claim a comprehensive presentation of the subject but have only tried to re-capture some of the essential results and pointed out their inter-connectivity.
References
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TL;DR: In this paper, the concept of two-photon coherent states is introduced for applications in quantum optics, which is a simple generalization of the well-known minimum-uncertainty wave packets.
Abstract: The concept of a two-photon coherent state is introduced for applications in quantum optics. It is a simple generalization of the well-known minimum-uncertainty wave packets. The detailed properties of two-photon coherent states are developed and distinguished from ordinary coherent states. These two-photon coherent states are mathematically generated from coherent states through unitary operators associated with quadratic Hamiltonians. Physically they are the radiation states of ideal two-photon lasers operating far above threshold, according to the self-consistent-field approximation. The mean-square quantum noise behavior of these states, which is basically the same as those of minimum-uncertainty states, leads to applications not obtainable from coherent states or one-photon lasers. The essential behavior of two-photon coherent states is unchanged by small losses in the system. The counting rates or distributions these states generate in photocount experiments also reveal their difference from coherent states.
1,661 citations
TL;DR: The properties of a unique set of quantum states of the electromagnetic field are reviewed in this article, and proposed schemes for the generation and detection of squeezed states as well as potential applications are discussed.
Abstract: The properties of a unique set of quantum states of the electromagnetic field are reviewed. These ‘squeezed states’ have less uncertainty in one quadrature than a coherent state. Proposed schemes for the generation and detection of squeezed states as well as potential applications are discussed.
1,501 citations
TL;DR: In this paper, the quadrature-phase amplitudes and two-mode squeezed states were introduced for analyzing two-photon devices, in which photons in the output modes are created or destroyed two at a time.
Abstract: This paper introduces a new formalism for analyzing two-photon devices (e.g., parametric amplifiers and phase-conjugate mirrors), in which photons in the output modes are created or destroyed two at a time. The key property of a two-photon device is that it excites pairs of output modes independently. Thus our new formalism deals with two modes at a time; a continuum multimode description can be built by integrating over independently excited pairs of modes. For a pair of modes at frequencies \ensuremath{\Omega}\ifmmode\pm\else\textpm\fi{}\ensuremath{\epsilon}, we define (i) quadrature-phase amplitudes, which are complex-amplitude operators for modulation at frequency \ensuremath{\epsilon} of waves ``cos[\ensuremath{\Omega}(t-x/c)]'' and ``sin[\ensuremath{\Omega}(t-x/c)]'' and (ii) two-mode squeezed states, which are the output states of an ideal two-photon device. The quadrature-phase amplitudes and the two-mode squeezed states serve as the building blocks for our formalism; their properties and their physical interpretation are extensively investigated.
631 citations
01 May 1985
TL;DR: A new formalism for analyzing two-photon devices, such as parametric amplifiers and phase-conjugate mirrors, is proposed, focusing on the properties and the significance of the quadrature-phase amplitudes and two-mode squeezed states.
Abstract: A new formalism for analyzing two-photon devices, such as parametric amplifiers and phase-conjugate mirrors, is proposed in part I, focusing on the properties and the significance of the quadrature-phase amplitudes and two-mode squeezed states. Time-stationary quasi-probability noise is also detailed for the case of Gaussian noise, and uncertainty principles for the quadrature-phase amplitudes are outlined, as well as some important properties of the two-mode states. Part II establishes a mathematical foundation for the formalism, with introduction of a vector notation for compact representation of two-mode properties. Fundamental unitary operators and special quantum states are also examined with an emphasis on the two-mode squeezed states. The results are applied to a previously studied degenerate limit (epsilon = 0).
539 citations
TL;DR: In this paper, it was shown that the states of the harmonic oscillator can be obtained from the coherent state of the coherent wave-packet, and it was also shown how a coherent state can be expanded in the basis of these states.
Abstract: Roy and Virendra Singh showed that the harmonic oscillator possesses an infinite string of exact shape-preserving coherent wave-packet states \ensuremath{\Vert}n,\ensuremath{\alpha}〉 having classical motion. In this paper it is shown that the states \ensuremath{\Vert}n,\ensuremath{\alpha}〉 could be obtained from the coherent state \ensuremath{\Vert}\ensuremath{\alpha}〉 and it is also shown how a coherent state \ensuremath{\Vert}\ensuremath{\alpha}〉 could be expanded in the basis of \ensuremath{\Vert}n,\ensuremath{\alpha}〉's. Further, the possibility of ``squeezing'' the state \ensuremath{\Vert}n〉 is investigated and the ``generalized squeezed coherent states'' are obtained. The squeezed coherent states for the displaced oscillator are also defined. The physical meaning of squeezing is also pointed out.
120 citations