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Squeezed States of Light

Partha Pratim Mondal

Published May 25, 2022• 0 citations
Publisher

Abstract

Light exists in several distinct quantum states that include photon number and coherent states. But these are not the only states of light, and others that are known to display unusual properties raise hopes for a deeper understanding of the quantum behavior at the classical-quantum barrier. In the previous chapter, we learned about two important states of light: the coherent and number states. In this chapter, we will deal with a special state of light called the squeezed state. As the name suggests, conjugate quantities/variables (such as intensity and phase) can be squeezed beyond their short-noise limit, obeying Heisenberg’s uncertainty principle. These specialized states of light have the distinct ability to measure variables (e.g., intensity) below the short-noise limit. Of course, this comes at the cost of increased uncertainty in the associated conjugate variable. In this chapter, we will explore these possibilities and briefly discuss techniques to generate such light. These specialized light sources find applications in ultrahigh precision measurement (gravitational-wave detection) and sophisticated instrumentation.

DOI
10.1063/9780735424517_008

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Light exists in several distinct quantum states that include photon number and coherent states. But these are not the only states of light, and others that are known to display unusual properties raise hopes for a deeper understanding of the quantum behavior at the classical-quantum barrier. In the previous chapter, we learned about two important states of light: the coherent and number states. In this chapter, we will deal with a special state of light called the squeezed state. As the name suggests, conjugate quantities/variables (such as intensity and phase) can be squeezed beyond their short-noise limit, obeying Heisenberg’s uncertainty principle. These specialized states of light have the distinct ability to measure variables (e.g., intensity) below the short-noise limit. Of course, this comes at the cost of increased uncertainty in the associated conjugate variable. In this chapter, we will explore these possibilities and briefly discuss techniques to generate such light. These specialized light sources find applications in ultrahigh precision measurement (gravitational-wave detection) and sophisticated instrumentation.
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.
As a direct result of the quantum nature of electromagnetic radiation, all forms of light exhibit inherent and unavoidable random fluctuations. Because these fluctuations reveal information about the nature of light and the underlying processes that generate it, they have received considerable attention since the time of Einstein. But they are also a source of noise that limits the accuracy with which information can be transmitted by a beam of light. Although experiments often still struggle with instrumental noise, some are quickly approaching the measurement limits set by the quantum-statistical nature of light. With the help of new techniques to “squeeze” the uncertainty of light, researchers can now conduct experiments with greater precision than possible with laser light. The generation of various forms of squeezed light in recent years has raised hopes for its application to such diverse areas as gravity-wave detection based on optical interferometry and reduced-error lightwave communications.
This chapter reviews theoretical and experimental aspects of non-classical states of light, e.g., squeezed states and number states. The definition of squeezed states and a review of their general properties is followed by a discussion of special kinds of squeezing, e.g., squeezed coherent states, displaced squeezed states, and amplitude or phase squeezing. An overview of photon counting statistics and robustness of squeezed states is followed by a theoretical model of their generation and a description of their experimental production. The chapter ends with a brief discussion of the experimental generation of number states, including methods for generation of single-photon states on demand, which have applications to quantum information processing.
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.
According to the Heisenberg uncertainty principle, the precision of any physical quantity measurement is limited by quantum fluctuation in general, which leads to the so-called standard quantum limit (SQL). The SQL can be beaten by using squeezed light, hence enhancing the measurement accuracy. Squeezed light is a typical nonclassical light, it exhibits reduced noise in one quadrature component. Since Caves proposed the scheme of phase measurement enhancement with squeezing, squeezed light has been used to enhance measurement precision in many areas. This review focuses on the following four kinds of precision measurements based on squeezed light: the measurements of relative phase, small lateral displacement and tilt, magnetic field, and clock synchronization. For all of these measurements, vacuum squeezing has been used to enhance measurement precision, while the types of squeezing (squeezing angle, transverse mode, polarization etc.) are different. For phase measurement, quadrature squeezing is injected into the conventionally unused input port of Mach-Zehnder interferometer (MZI) or Michelson interferometer (MI). For displacement or tilt measurement, a vacuum squeezing beam of a special transverse mode is coupled into an intense coherent beam, yielding a spatial-squeezed light whose transverse position or tilt angle noise is lower than that of a classical light beam. Based on the Faraday effect of polarization rotation, the magnetic field can be detected precisely. The precision can be increased further by using the polarization squeezing. The polarization squeezing can be generated by coupling two orthogonal polarized beams together, a coherent beam and a vacuum squeezed beam. Various polarization squeezing can be illustrated on the Poincaré sphere. Finally, in the clock synchronization based on the optical frequency comb, squeezed light can be used to enhance the time measurement precision. A theoretical scheme with multimode squeezing of supermode (a kind of mode describing the frequency mode of a pulse laser beam) is introduced. The squeezing has extensively been applied into the quantum precision measurements such as gravitational wave detection as well as biological measurement and will play a more important role in the near future.