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Journal of Modern Optics

Generation of amplitude squeezed states of light from phase squeezed coherent states

Kasivishvanathan Sundar

Published Apr 1, 1996• 3 citations
Publisher

Abstract

We propose a scheme to generate a displaced macroscopic superposition of phase squeezed coherent states by incorporating an optical parametric oscillator (OPO) and a nonlinear Kerr medium in a Mach-Zhender interferometer configuration. We show that the phase squeezed coherent state generated by the OPO evolves into a macroscopic superposition of phase squeezed coherent states on spending a specific amount of time inside a Kerr medium. The phase space displacement is achieved by the interference of the intense reference beam with the signal in the final beam splitter of the interferometer. The noise of the reference beam contaminating the signal is prevented by making this beam splitter highly reflective. We have calculated the photon number uncertainty of the outcoming beam and have shown that it is smaller than the usual amplitude squeezed coherent state's value.

DOI
10.1080/09500349608232785

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We propose a scheme to generate a displaced macroscopic superposition of phase squeezed coherent states by incorporating an optical parametric oscillator (OPO) and a nonlinear Kerr medium in a Mach-Zhender interferometer configuration. We show that the phase squeezed coherent state generated by the OPO evolves into a macroscopic superposition of phase squeezed coherent states on spending a specific amount of time inside a Kerr medium. The phase space displacement is achieved by the interference of the intense reference beam with the signal in the final beam splitter of the interferometer. The noise of the reference beam contaminating the signal is prevented by making this beam splitter highly reflective. We have calculated the photon number uncertainty of the outcoming beam and have shown that it is smaller than the usual amplitude squeezed coherent state's value.
The evolution of a quadrature-squeezed state through a Kerr medium is studied from the point of view of amplitude squeezing. We propose a Mach-Zehnder interferometer configuration, which incorporates a squeeze- state generator and a nonlinear Kerr medium, to generate and subsequently displace these states. The displaced states show amplitude squeezing for a proper choice of the initial quadrature squeezed state, and we study two such cases here in detail. In the limit where the evolution through a Kerr medium results in a macroscopic superposition, an initial phase-squeezed coherent state shows significant amplitude squeezing, and we have shown that the photon-number uncertainty 〈(\ensuremath{\Delta}n^)2{)}^{2})2〉 can be minimized to a value smaller than 〈n^〉2/3{\mathrm{〉}}^{2/3}〉2/3. On the other hand, an initial quadrature-squeezed state, whose direction of squeezing is along the direction of excitation, upon evolving through a Kerr medium for a suitable small duration of time shows substantial amplitude squeezing for an appropriate displacement, and we show that the photon-number uncertainty in this case can be minimized to 〈n^〉1/5{\mathrm{〉}}^{1/5}〉1/5, which is far below the previously achieved limits. \textcopyright{} 1996 The American Physical Society.
We propose here a quantum state obtained by evolving a quadrature-squeezed state through a Kerr medium. We give a Mach-Zhender interferometer configuration to generate and displace this state to an appropriate position in phase space. The displaced state is highly amplitude squeezed when the direction of squeezing of the initial quadrature squeezed state is along the direction of coherent excitation. We show that the photon number uncertainty $〈(\ensuremath{\Delta}\stackrel{^}{n}{)}^{2}〉<〈\stackrel{^}{n}{〉}^{1/5}$, which is far below the previously achieved limits in similar schemes.
Light in which the quantum fluctuations have been squeezed is often proposed as a means of obtaining an improved phase reference compared to that available from coherent light. Such a phase reference contains information about the phase of the squeezed light, so it is important to calculate the limits to the amount of ``phase information'' available. I define a phase resolution and show how this scales as we increase the number of photons available when using squeezed light generated by a parametric oscillator. Simple schemes for creating squeezed coherent light using a beam-splitter and an interferometer are analyzed, and it is shown that the results agree with earlier claims [Kinsler] that when using squeezed coherent light as a phase reference, the gain is not one of improved accuracy, but of lower power.
High-quality squeezed light is an important resource for a variety of applications. Multiple methods for generating squeezed light are known, having been demonstrated theoretically and experimentally. However, the effectiveness of these methods—in particular, the inherent limitations to the signals that can be produced—has received little consideration. Here we present a comparative theoretical analysis for generating a highly displaced squeezed light from a linear optical method—a beamsplitter mixing a squeezed vacuum and a strong coherent state—and well-studied parametric amplification methods including an optical parametric oscillator, an optical parametric amplifier, and a dissipative optomechanical squeezer seeded with coherent states. We show that the quality of highly displaced squeezed states that can be generated using these methods is limited on a fundamental level by the physical mechanism utilized; across all methods there are significant trade-offs between displacement, squeezing, and overall uncertainty. We explore the nature and extent of these trade-offs specific to each mechanism and identify the optimal operation modes for each. Finally, we identify the conditions for minimum-uncertainty squeezing in arbitrary parametric amplifying systems and show that displacing the output signal will in general violate these conditions, adding noise and degrading squeezing.
We suggest an all-optical scheme to generate entangled superposition of a single photon with macroscopic entangled states for testing macroscopic realism. The scheme consists of source of single photons, a Mach-Zehnder interferometer in routes of which a system of coupled-down converters with type-I phase matching is inserted, and a beam splitter for the other auxiliary modes of the scheme. We use quantization of the pumping modes, depletion of the coherent states passing through the system, and interference effect in the pumping modes in the process of erasing which-path information of the single-photon on exit from the Mach-Zehnder interferometer. We show the macroscopic fields of the output superposition are distinguishable states. This scheme generates macroscopic entangled state that violates Bell's inequality. Moreover, the detailed analysis concerning change of amplitudes of entangled superposition by means of repeating this process many times is accomplished. We show our scheme works without photon number resolving detection and it is robust to detector inefficiency.
We study the statistical and phase properties of the output states of a Mach-Zehnder interferometer with a nonlinear Kerr medium in one of its arms. The combination of nonlinearity and displacement produced by the interferometer generates output states (displaced Kerr states) that, unlike those derived from a Kerr medium alone (Kerr states), do not necessarily retain the photon statistics of the initially coherent field. As the parameter characterizing the nonlinear medium is varied, the statistics of the output field vary from sub-Poissonian to super-Poissonian. The photon-number distributions of these states are rationalized by examining their quasiprobability distributions, which vary from banana-shaped for sub-Poissonian statistics to complicated interference structures for highly super-Poissonian statistics. The number-phase properties of the Kerr and displaced Kerr states are studied for the case of small photon numbers (relevant to cavity quantum electrodynamics) using a methodology based on the Pegg-Barnett formalism. In particular, we determine the range of parameters for which the states are minimum-uncertainty states and whether they are squeezed with respect to photon number and phase, drawing a distinction between a sub-Poissonian nature and number squeezing. Finally, we find that sub-Poissonian statistics can coexist with quadrature squeezing for a range of parameters.