Squeezed states in phase-sensing interferometers

Bondurant, Roy S.; Shapiro, Jeffrey H.

doi:10.1103/physrevd.30.2548

Cited by 269 publications

(139 citation statements)

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“…The phase sensitivity of interferometers is believed to be limited by quantum fluctuations [12], and the phase sensitivity of various interferometers has been explored for different types of input states, such as squeezed states [12,13], and number states [14,15,16,17,18,19,20,21,22]. In all the above cases, the phase sensitivity ∆φ has been discussed in terms of two limits, known as the standard limit, ∆φ SL = 1/ √ N , and the Heisenberg limit [23], ∆φ HL = 1/N , where N is the number of particles that enter the interferometer during each measurement cycle.…”

Section: Introductionmentioning

confidence: 99%

Fidelity of quantum interferometers

Bahder

Lopata

2006

Phys. Rev. A

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For a generic interferometer, the conditional probability density distribution, p(φ|m), for the phase φ given measurement outcome m, will generally have multiple peaks. Therefore, the phase sensitivity of an interferometer cannot be adequately characterized by the standard deviation, such as ∆φ ∼ 1/ √ N (the standard limit), or ∆φ ∼ 1/N (the Heisenberg limit). We propose an alternative measure of phase sensitivity-the fidelity of an interferometer-defined as the Shannon mutual information between the phase shift φ and the measurement outcomes m. As an example application of interferometer fidelity, we consider a generic optical Mach-Zehnder interferometer, used as a sensor of a classical field. We find the surprising result that an entangled N00N state input leads to a lower fidelity than a Fock state input, for the same photon number. Introduction.Phase sensitivity of interferometers has been a topic of research for many years because of interest in the fundamental limitations of measurement [1, 2], gravitational-wave detection [3], and optical [4,5], atom [6], and Bose-Einstein condensate(BEC)-based gyroscopes [7,8,9]. Recently, applications to sensors are being explored [10,11].The phase sensitivity of interferometers is believed to be limited by quantum fluctuations [12], and the phase sensitivity of various interferometers has been explored for different types of input states, such as squeezed states [12,13], and number states [14,15,16,17,18,19,20,21,22]. In all the above cases, the phase sensitivity ∆φ has been discussed in terms of two limits, known as the standard limit, ∆φ SL = 1/ √ N , and the Heisenberg limit[23], ∆φ HL = 1/N , where N is the number of particles that enter the interferometer during each measurement cycle. These arguments are based on results of standard estimation theory [24] which connects an ensemble of measurement outcomes, m i , i = 1, 2, · · · , M , with corresponding phases, φ i , through a theoretical relation m = m(φ). An example of the theoretical relation associated with some quantum observable is m(φ) = φ| m|φ , where the state is parameterized by a single parameter φ. Standard estimation theory predicts that the standard deviation, ∆φ, of the probability distribution for the phase φ, is related to the standard deviation in the measurements, ∆m, by [24]

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Section: Introductionmentioning

confidence: 99%

Fidelity of quantum interferometers

Bahder

Lopata

2006

Phys. Rev. A

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“…Following this line, in Refs. [3,4] the Michelson interferometer with Kerr media placed into the arm cavities has been analyzed. It was shown that Kerr media inside the arms can cancel radiation pressure noise at some sideband frequencies.…”

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confidence: 99%

Optical Transfer Functions of Kerr Nonlinear Cavities and Interferometers

et al. 2005

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We present the optical transfer functions for third-order nonlinear cavities that involve an optical carrier frequency and its modulation sideband fields. Our approach is based on linearized transformations and provides a convenient tool to calculate squeezed light sources as well as complex interferometer topologies, containing subsystems that involve intensity dependent phase shifts, i.e., optical Kerr media. As the result we present the noise spectral density of a Michelson interferometer with Kerr nonlinear arm cavities and resonant sideband extraction and find that quantum noise can be squeezed by arbitrary amounts even outside the cavity linewidth. Such a system might apply for future gravitational wave detectors or simply for a continuous wave source of squeezed states. DOI: 10.1103/PhysRevLett.95.193001 PACS numbers: 42.50.Dv, 03.65.Ta The input and output of damped quantum optical systems have been successfully described by quantum Langevin equations. This approach led to the first correct description of traveling wave squeezed light [1]. However, this approach is not easy to deal with due to its nonlinear operator nature. Especially the description of complex optical systems, like advanced laser interferometers that comprise a detuned resonant sideband extraction (RSE) cavity [2] in combination with radiation pressure and nonlinear media, is a nontrivial task. Fortunately, for most practical purposes the quantum noise can be assumed to be small compared to the field's expectation value and the problem can be linearized. Following this line, in Refs. [3,4] the Michelson interferometer with Kerr media placed into the arm cavities has been analyzed. It was shown that Kerr media inside the arms can cancel radiation pressure noise at some sideband frequencies.The interest in nonclassical techniques has been increasing considerably during recent years. This is partly due to the fact that quantum noise will be one of the major noise sources in second-generation interferometric gravitational wave (GW) detectors (e.g., Advanced LIGO [5]). It is therefore very likely that third-generation detectors will exploit quantum correlations, i.e., quantum-nondemolition techniques [6,7] and nonlinear optics might become one of the standard tools.In this Letter we reinvestigate the Kerr medium inside the arm cavities of a Michelson interferometer and present signal and noise transfer functions. For the first time, to our best knowledge, we report the noise spectral density of a Kerr-effect enhanced Michelson interferometer with RSE. We apply a theoretical approach which can easily be extended to even more complex optical systems. Our formalism is based on linearized transformations of the quadrature fields within two-photon quantum optics [8] which has previously been used to describe ponderomotive squeezing [6] and the optical spring effect [5]. In this formalism the transfer functions map quadrature amplitudes which act at positive modulation frequencies around an optical carrier frequency ! 0 . It is well-known that...

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“…The application of squeezed states of light in high-precision interferometry often serves as a prominent example [3,4,5,6]. Here the improved precision results from quantum noise reduction due to a specific superposition of photon number states.…”

Section: Introductionmentioning

confidence: 99%