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Conference on Lasers and Electro-Optics Europe & European Quantum Electronics Conference (CLEO/Europe-EQEC)

Suppression of quantum noise in optical physics

P. L. Knight

Published Jan 1, 1994• 0 citations
Publisher

Abstract

The search for optical fields with quantum fluctuations less than that of a perfectly coherent signal has reopened questions of appropriate signatures of non-classicality. Squeezed light fields have phase dependent noise that for some phase angles can be substantially less than the normal vacuum fluctuations. Sub-Poissonian light has photon number fluctuations below those expected from naive "shot noise" considerations. In this talk, I will review the progress made in understanding non-classical light, and discuss measures of non-classicality.

DOI
10.1364/cleo_europe.1994.tutorial.e

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•Nov 1, 1987•0 citations
The search for optical fields with quantum fluctuations less than that of a perfectly coherent signal has reopened questions of appropriate signatures of non-classicality. Squeezed light fields have phase dependent noise that for some phase angles can be substantially less than the normal vacuum fluctuations. Sub-Poissonian light has photon number fluctuations below those expected from naive "shot noise" considerations. In this talk, I will review the progress made in understanding non-classical light, and discuss measures of non-classicality.
Current laser systems have phase and amplitude fluctuations which are partially quantum in origin. The amplitude fluctuations of a highly stabilized laser are shot noise limited, that is they have quantum fluctuations due to the Poissonian fluctuations of photons in a coherent state. These photon number fluctuations have been shown to have an origin in the incoherent pumping mechanism used for standard lasers. It has recently been demonstrated experimentally that by suppressing the amplitude fluctuations of the pump a laser output with reduced amplitude fluctuations is possible. The phase fluctuations in a laser are due to phase diffusion and are substantially above the quantum limit. Techniques to reduce the laser phase fluctuations have been proposed making use of correlated spontaneous emission.
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.
The minimum resolvable signal in sensing and metrology platforms that rely on optical readout fields is increasingly constrained by the standard quantum limit, which is determined by the sum of photon shot noise and back-action noise. A combination of back-action and shot noise reduction techniques will be critical to the development of the next generation of sensors for applications ranging from high-energy physics to biochemistry and for novel microscopy platforms capable of resolving material properties that were previously obscured by quantum noise. This Perspective reviews the dramatic advances made in the use of squeezed light for sub-shot-noise quantum sensing in recent years and highlights emerging applications that enable new science based on signals that would otherwise be obscured by noise at the standard quantum limit.
High quality light, whenever coherent light and nonclassical light, is more and more widely used in many filed.The coherent state behave minimum classical noise and better coherence, is mostly important light in quantum information, precise measurement and quantum metrology etc.In quantum information and quantum optics, a coherent light is used to entanglement generation (Ou, Z. et al. 1992), quantum teleportation (Furusawa, A. et al. 1998A.et al. ), quantum computation (Menicucci, N. et al. 2006) and quantum secret sharing (Lance, A. et al. 2004).The quiet laser beam, shot noise limited laser beam is important in above application.In the past 20 years there has been much interest in the generation and application of various nonclassical light sources, such as squeezed-state entanglement, quantum-correlated twin beams, and sub-poissonian light, for which improved signal-to-noise ratios and measurement precision beyond the quantum-noise limit are anticipated.In particular, subpoissonian light is a promising light source in quantum information and optical communication because of its communication capacity (
The author reviews methods for generating sub-Poissonian light and related concepts. This light has energy fluctuations reduced below the level which corresponds to a classical Poissonian process (shot-noise level). After an introduction to the concept of nonclassical light, an overview is given of the main methods of quantum-noise reduction. Sub-Poissonian processes are exemplified in different areas of optics, ranging from single-atom resonance fluorescence to nonlinear optics, laser physics, and cavity quantum electrodynamics. Emphasis is placed on the conceptual foundations, and on developments in laser theory that lead to the possibility, already demonstrated experimentally, of linewidth narrowing and sub-Poissonian light generation in lasers and masers. The sources of quantum noise in these devices are analyzed, and four noise-suppression methods are discussed in detail: regularization of the pumping, suppression of spontaneous-emission noise, nonadiabatic evolution of the atomic variables, and twin-beam generation.
The nature of phase noise in quantum optics is analyzed. In an experiment involving the measurement of the electromagnetic field the two quantities of interest are the energy and phase of the field. However, measurements of the quantities produce quantum fluctuations. The quantum fluctuations are regarded as noise in the treatment presented here. The quantum system is represented by a probability distribution, the Wigner function, and the quantum fluctuations are treated as stochastic noise associated with the quantity being measured. The difficulties of associating a quantum operator with the phase of the system are reviewed and the related energy-phase uncertainty relation is discussed. The alternate interpretation of the phase noise of a quantum system as being the classical phase noise of the Wigner function is presented. In particular the energy and phase noise of the vacuum state, the coherent state, the squeezed state and the squeezed vacuum are discussed in this way. The squeezed states of light are minimum uncertainty states with respect to the quadrature operators and exhibit noise of one quadrature below the noise level associated with the vacuum. The reduced noise level in one quadrature of the field underlies the importance of squeezed states in many practical applications where there is a need to reduce the quantum noise of one quadrature of coherent light. The periodic phase operator eliminates the difficulties associated with the multivalued nature of phase. The analysis of the vacuum and intense coherent state of Carruthers and Nieto by employing periodic phase operators is reviewed, particularly with respect to the energy-phase uncertainty relations and we generalize the approach to develop a phase operator analysis of the squeezed state in the intense field and vacuum limits. We demonstrate here for the first time that the phase operator is simply related to the phase of the squeezed state in the intense field limit and that the squeezed state is approximately an energy-phase minimum uncertainty state in the low-squeezing limit. Also we enlarge on previous work to demonstrate that the phase operator corresponds simply and unambiguously to the phase of the squeeze parameter for the strongly squeezed vacuum and the intensely squeezed vacuum is an energy-phase minimum uncertainty state for some values of phase. The occurrence of squeezing for the case of two coupled quantum oscillators is presented. The system consisting of one mode of the electromagnetic field coupled to a spinless nonrelativistic electron subjected to an harmonic potential is represented by two coupled harmonic oscillators. The dynamics are compared for the case that the rotating wave approximation is employed and for the case that the counter-rotating terms are included. These calculations have not been performed before. The parametric amplifier Hamiltonian with a nonresonant coupling is also studied in order to provide insight into the effects of the counter-rotating terms. Squeezing of the field produced by the electron is a consequence of the inclusion of the counter-rotating terms. The case of a spinless nonrelativistic electron subject to an harmonic potential and coupled to a continuum of electromagnetic field modes is also considered. The case of two coupled oscillators discussed above is generalized by replacing the oscillator which represents the single-mode field by a bath of oscillators. The effects of including counter-rotating terms and of ignoring the counter - rotating terms in the Hamiltonian are compared. The interaction is assumed to produce a frequency shift and an exponential damping term for the oscillating electron. The frequency shift is assumed to be small in either case and so the Wigner-Weisskopff approximation is employed to solve the equations of motion. We demonstrate the new results that dissipation-induced phase-dependent noise is a consequence of including the counter-rotating terms and that the noise is phase-independent for the case that the counterrotating terms are excluded. The relation between these results and recent work on quantum tunnelling in superconducting quantum interference devices is discussed. We conclude by suggesting further research related to the work in this thesis.