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Nonlinear Optics

Squeezing with fiber Sagnac loop and sub-shot-noise measurement

H. A. Haus, K. Bergman, Luc Boivin, Masataka Shirasaki, Erich P. Ippen

Published Dec 17, 2002• 0 citations
Publisher

Abstract

Squeezed states of light are minimum uncertainty states for which the mean square fluctuations in phase and in quadrature with respect to a reference signal are unequal. Among other interesting properties, they provide improved sensitivity of optical interferometric phase measurements. To understand this potential, one must note that quantum theory imposes measurement uncertainty only on a pair of noncommuting variables; the measurement of any one quantum observable could be done with no uncertainty.>

DOI
10.1109/nlo.1994.470801

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Squeezed states of light are minimum uncertainty states for which the mean square fluctuations in phase and in quadrature with respect to a reference signal are unequal. Among other interesting properties, they provide improved sensitivity of optical interferometric phase measurements. To understand this potential, one must note that quantum theory imposes measurement uncertainty only on a pair of noncommuting variables; the measurement of any one quantum observable could be done with no uncertainty.>
Squeezed states of the electromagnetic field are characterized by a reduction of fluctuations for one of two quadrature phase amplitudes below the level of fluctuations for the vacuum state. This reduction is a manifestly quantum or nonclassical feature which is of great interest in its own right but also potentially important for precision measurement with sensitivity beyond the shot-noise or vacuum-state limit. We describe three different experiments in which squeezed light has been generated in our laboratory involving parametric downconversion, intracavity frequency doubling, and optical bistability with two-state atoms. By employing the squeezed light produced by a subthreshold optical parametric oscillator, we have achieved improvements in sensitivity beyond the vacuum-state limit for the detection of both phase and amplitude changes of the electromagnetic field. An alternate route to sensitivity beyond the vacuum-state limit is through quantum nondemolition measurement, where we have suggested and are implementing a scheme involving parametric conversion and polarization mixing.
We showed in Section 5.2 of the present chapter that according to quantum theory the value of the electric field of an electromagnetic wave could not be predicted to arbitrarily high precision, this being a consequence of the uncertainty relation satisfied by the two quadrature components of the field (Equation 5.32), which imposed a finite limit on the product of their variances. This limit is more than an abstract theoretical limit; it is often the overriding factor determining the resolution of high-precision optical measurements. In such situations measurements by photodetectors on the field exhibit uncontrollable fluctuations of quantum origin known as quantum noise . Fortunately, as we shall show in this complement, it is possible to overcome this by using non-classical states of the radiation field, namely the squeezed states , provided measurements are made of a single one of a pair of conjugate field variables. A field mode prepared in such a state exhibits reduced quantum noise in one of the variables at the expense of increased noise in the other, so that the uncertainty relation involving their variances is still satisfied. The potential of such states for increasing the obtainable precision of optical measurements is self-evident. However, the practical realization of the potential benefits requires delicate experimental techniques that we describe only briefly here.
The origin of quantum noise is addressed and it can be eliminated when the quantum state is optimally prepared for the single measured observable. Minimum uncertainty states are reviewed using Q (α) -representation, which include squeezed states and number-phase minimum uncertainty states. Squeezing is a concept of trading quantum uncertainties between two conjugate observables to optimize the state for the measurement. Need for optical nonlinearity to achieve squeezing is induced. Principles and experimental results for squeezing quadrature amplitude and photon number are delineated. Applications to optical communications and optical precision measurement are briefly stated.
A squeezed state of light is usually taken to mean a state in which the fluctuations of one of the quadratures are below the level associated with a coherent or vacuum state. These squeezed fluctuations are phase sensitive in the sense that they vary periodically as the field evolves, but the relationship between squeezing and phase fluctuations is not trivial. While squeezed states can exhibit an arbitrarily low level of phase fluctuations, the phase states, which are eigenstates of the Hermitian optical phase operator are not themselves quadrature squeezed. A phasesqueezed state is one with a lower level of phase fluctuations than a coherent state with the same mean photon number. Phase squeezing is fundamentally different from quadrature squeezing in much the same way that sub-Poissonian photon statistics is different. For this reason optimally squeezed states and states with minimum phase noise will be distinct. We derive the form of the states which minimum phase noise for a given intensity. These have an Airy function behavior for the photon number probability distribution. These phase squeezed states have a far better phase resolution than coherent states of similar intensity, but do not seem to offer a significant reduction of phase fluctuations compared with conventional squeezed states.
Well-stabilized lasers emit radiation that is a close approximation to a coherent state: a classical mean field which varies sinusoidally in time at optical frequency ω0, superposed with broad-band noise fields due to the field's quantum uncertainty in its ground state (i.e. vacuum fluctuations). When detected by a standard photodetector, the interference between these vacuum fields and the coherent mean field causes the noise floor commonly referred to as the "shot-noise limit." The vacuum noise also causes fluctuations in the phase of the beam that are independent and uncorrelated with the amplitude fluctuations, and to which photodetectors are insensitive. The amplitude and phase fluctuations of the field can be represented by quadrature amplitudes X ^ A ( δ ) and X ^ ϕ ( δ ) which are the Fourier components of amplitude and phase modulation or fluctuation at a particular modulation frequency δ. These quadrature amplitudes are non-commuting quantum observables which obey the uncertainty principle.
One of the most promising applications for squeezed light is interferometry beyond the shot-noise limit (SNL). To date, only squeezed light generated by parametric down-conversion has been used to improve interferometer sensitivity. Remarkable results have been achieved with this approach, including applications to large-scale gravitational wave detectors. On the other hand, there exists a potentially more robust way to generate squeezed light, that is, using the optical Kerr effect. It occurs almost for free in optical fibers and requires no phase matching. However, no interferometer sensitivity enhancement has been demonstrated so far using this method. One of the reasons for that is that the uncertainty distribution of a Kerr-squeezed state in phase space is tilted with respect to the amplitude or phase quadratures. Additional obstacles include Raman and guided acoustic wave Brillouin scattering in fibers.