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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Quantum Optics And Nonlinear Interactions In Optical Fibers

Robert M. Shelby, M. D. Levenson

Published Jan 1, 1987• 0 citations
Publisher

Abstract

A stabilized laser emits a light beam in a coherent state: a light field with properties very similar to a classical field, but with quantum zero-point fluctuations (vacuum noise) of the field superposed. The nonlinear refractive index of optical fibers can be used to alter the quantum statistics of the light to produce a beam with non-classical properties: a squeezed state. Upon detection, squeezed states exhibit a noise level which is phase-dependent and which can be well below the coherent state level ("shot-noise limit"). The nonlinear refractive index also provides a means for experimental demonstration of the related concept of "quantum non-demolition detection": The measurement of a quantum observable without adding uncertainty to that variable.

DOI
10.1117/12.966905

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A stabilized laser emits a light beam in a coherent state: a light field with properties very similar to a classical field, but with quantum zero-point fluctuations (vacuum noise) of the field superposed. The nonlinear refractive index of optical fibers can be used to alter the quantum statistics of the light to produce a beam with non-classical properties: a squeezed state. Upon detection, squeezed states exhibit a noise level which is phase-dependent and which can be well below the coherent state level ("shot-noise limit"). The nonlinear refractive index also provides a means for experimental demonstration of the related concept of "quantum non-demolition detection": The measurement of a quantum observable without adding uncertainty to that variable.
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.
Optical solitons are pulses that propagate in optical fibers without temporal or spectral distortion, owing to balancing of the second-order dispersion of the refractive index by nonlinear self-phase modulation induced by the intensity-dependent refractive index. Classically, this stationary, distortion-free propagation requires only the proper choice of pulse width and shape for a given pulse energy. However, quantum mechanical zero-point fluctuations of the amplitude and phase of the optical pulse limit the precision with which this pulse shape can be produced. These quantum fluctuations do not undergo stationary propagation but, rather, evolve because of dispersion and self-phase modulation, As a soliton pulse propagates, this zero-point or vacuum noise associated with the pulse evolves into squeezed noise owing to self-phase modulation in the fiber.1,2
Parametric interactions such as four wave mixing have been predicted to produce states of the radiation field where the quantum fluctuations in one phase quadrature are less than those of a coherent state.1 These “squeezed states” have proved remarkably difficult to generate and detect, not least because of the presence of additional classical noise in many laser sources and parametric devices. We have now demonstrated the reduction of classical fluctuations by means of four wave mixing in an optical fiber under conditions very similar to those needed to demonstrate squeezed state generation. This success reinforces the plausibility of related quantum noise experiments, and has implications for fiber optic communications.
Optical solitons are pulses that propagate in optical fibers without temporal or spectral distortion, owing to balancing of the second-order dispersion of the refractive index by nonlinear self-phase modulation induced by the intensity-dependent refractive index. Classically, this stationary distortion-free propagation only requires the proper choice of pulse width and shape for a given pulse energy. However, quantum fluctuations do not undergo stationary propagation but rather evolve due to dispersion and self-phase modulation. As a soliton pulse propagates, zero-point or vacuum noise associated with the pulse evolves into squeezed noise. Vacuum fluctuations are responsible for the fundamental detector noise floor known as the shot noise limit. Reduction of the noise in the detection of squeezed soliton pulses has achieved a noise level 34% below this limit. In optical fibers, thermal fluctuation of the refractive index limit the noise reduction that can be achieved by adding phase fluctuations in excess of the vacuum noise. At low frequencies thermal noise originates from local structural dynamics of fused silica which produces a 1/f power spectrum and from guided acoustic wage Brillouin scattering which modulates the refractive index at frequencies characteristic of the fiber structure. The bandwidth of these fluctuations is ~2 GHz; and for soliton pulses with spectral bandwidth much >2 GHz, we have shown that this noise can be made insignificant. For very short pulses, however, noise from Raman scattering must be considered. Recent calculations incorporating this noise mechanism are compared with experiment.
Optical fibers offer considerable advantages over bulk nonlinear media for the generation of squeezed states. This thesis reports on experimental investigations of reducing quantum noise by means of squeezing in nonlinear fiber optic interferometers. Fibers have low insertion loss which allows for long interaction lengths. High field intensities are easily achieved in the small cores of single mode fibers. Additionally, the nonlinear process employed is self phase modulation or the Kerr effect, whose broad band nature requires no phase matching and can be exploited with ultra-short pulses of high peak intensity. All these advantageous features of fibers result in easily obtained large nonlinear phase shifts and subsequently large squeezing parameters. By the self phase modulation process a correlation is produced between the phase and amplitude fluctuations of the optical field. The attenuated or squeezed quadrature has a lower noise level than the initial level associated with the coherent state field before propagation. The resulting reduced quantum noise quadrature can be utilized to improve the sensitivity of a phase measuring instrument such as an interferometer.
This chapter is a short summary of recent developments concerning quantum noise. A quantum state is said to be squeezed when the fluctuations of one observable have been reduced below that of the vacuum state, that is, the ‘shot-noise’ level of the coherent state. Squeezed states are detected using the technique known as balanced homodyne detection. The chapter reviews the reductions in phase and amplitude fluctuations of a squeezed state and discusses their use in interferometry and spectroscopy. The phase-dependent nature of the squeezed field results in line-narrowing of the incoherent spectrum for particular phase choices while other choices of phase result in line-broadening. Interferometry with squeezed light as well as quantum non-demolition measurements are attempting to assess quantum measurement limits in order to further extend the experimental manipulation of light.