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Estado de vácuo comprimido para a luz: um questionamento sobre sua construção experimental

Tamíris R. Calixto

Published Aug 14, 2018• 0 citations
OpenAlex

Abstract

Coherent states are usually used to describe the state of a laser field in experiments for the generation and detection of squeezed states, in particular for the squeezed vacuum state. Nevertheless, the state of a laser field is better described by a statistical mixture of coherent states with random phases or, similarly, by a statistical mixture of Fock states.In this sense, the present works aim was to describe the experiment of generation of the squeezed vacuum state without using coherent states to describe the laser field. For the purpose of a first analysis, the state of the laser light was considered to be in a Fock state. Subsequently, for a more realistic description, a statistical mixture of Fock states is considered to describe the output state of the laser. From the correspondence between a statistical mixture of coherent states with random phases and a statistical mixture of Fock states, it is possible to obtain the experimental results without actually generating squeezedstates, since squeezing in a specific quadrature is not obtained due to the randomness of the laser field phase. This raises a question whether, in fact, the experimental generation of the squeezed vacuum states has already occurred.

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Coherent states are usually used to describe the state of a laser field in experiments for the generation and detection of squeezed states, in particular for the squeezed vacuum state. Nevertheless, the state of a laser field is better described by a statistical mixture of coherent states with random phases or, similarly, by a statistical mixture of Fock states.In this sense, the present works aim was to describe the experiment of generation of the squeezed vacuum state without using coherent states to describe the laser field. For the purpose of a first analysis, the state of the laser light was considered to be in a Fock state. Subsequently, for a more realistic description, a statistical mixture of Fock states is considered to describe the output state of the laser. From the correspondence between a statistical mixture of coherent states with random phases and a statistical mixture of Fock states, it is possible to obtain the experimental results without actually generating squeezedstates, since squeezing in a specific quadrature is not obtained due to the randomness of the laser field phase. This raises a question whether, in fact, the experimental generation of the squeezed vacuum states has already occurred.
Coherent states are normally used to describe the state of a laser field in experiments that generate and detect squeezed states of light. Nevertheless, since the laser field absolute phase is unknown, its quantum state can be described by a statistical mixture of coherent states with random phases, which is equivalent to a statistical mixture of Fock states. Here we describe single-mode squeezed vacuum experiments using this mixed quantum state for the laser field. Representing the laser state in the Fock basis, we predict the usual experimental results without using the squeezing concept in the analysis and concluding that no squeezed state is generated in the experiments. We provide a general physical explanation for the noise reduction in the experiments in terms of a better definition of the relative phase between the signal and local oscillator fields. This explanation is valid in any description of the laser field (in terms of coherent or Fock states), thus providing a deeper understanding of the phenomenon.
A laser, be it an optical laser or an atom laser, is an open quantum system that produces a coherent beam of bosons (photons or atoms, respectively). Far above threshold, the stationary state ${\ensuremath{\rho}}_{\mathrm{ss}}$ of the laser mode is a mixture of coherent-field states with random phase, or, equivalently, a Poissonian mixture of number states. This paper answers the question: can descriptions such as these, of ${\ensuremath{\rho}}_{\mathrm{ss}}$ as a stationary ensemble of pure states, be physically realized? Here physical realization is as defined previously by us [H. M. Wiseman and J. A. Vaccaro, Phys. Lett. A 250, 241 (1998)]: an ensemble of pure states for a particular system can be physically realized if, without changing the dynamics of the system, an experimenter can (in principle) know at any time that the system is in one of the pure-state members of the ensemble. Such knowledge can be obtained by monitoring the baths to which the system is coupled, provided that coupling is describable by a Markovian master equation. Using a family of master equations for the (atom) laser, we solve for the physically realizable (PR) ensembles. We find that for any finite self-energy $\ensuremath{\chi}$ of the bosons in the laser mode, the coherent-state ensemble is not PR; the closest one can come to it is an ensemble of squeezed states. This is particularly relevant for atom lasers, where the self-energy arising from elastic collisions is expected to be large. By contrast, the number-state ensemble is always PR. As the self-energy $\ensuremath{\chi}$ increases, the states in the PR ensemble closest to the coherent-state ensemble become increasingly squeezed. Nevertheless, there are values of $\ensuremath{\chi}$ for which states with well-defined coherent amplitudes are PR, even though the atom laser is not coherent (in the sense of having a Bose-degenerate output). We discuss the physical significance of this anomaly in terms of conditional coherence (and hence conditional Bose degeneracy).
Quantum statistical properties of laser light have been extensively studied for the last thirty years by using an operator Langevin equation, a density operator master equation, and a quantum mechanical Fokker-Planck equation. It has been generally accepted among physicists and quantum electronics engineers that an ideal laser operating at far above the threshold generates a coherent state of light. Various experimental facts such as the Poissonian photoelectron statistics, the shot noise limited photocurrent fluctuations, and the Gaussian distributions of optical homodyne detector output seem to support this. However, recent careful studies on a semiconductor laser have revealed that a semiconductor laser does not necessarily produce a coherent state of light, but generates a number-phase squeezed state, in which the photon-number noise is smaller than the standard quantum limit (shot noise limit or Poisson limit). This paper reviews the theoretical and experimental aspects of number-phase squeezed state generation by a semiconductor laser.
The amplitude and phase of all light fields are subject to fluctuations. Much of this irregularity arises from random and uncontrolled changes that occur in any light source and lead to random changes in the light wave's frequency and amplitude. Most of these factors can in principle be eliminated by a careful design of the light source. Even if all of these defects in the source are removed, however, light fields are still subject to fluctuations arising from the laws of quantum mechanics. Even in a highly stabilized laser, the resulting coherent electromagnetic field has an uncertainty in the phase and magnitude of its amplitude. All conventional sources of light fields have at least this noise level, which, in a fully quantum description, arises from vacuum fluctuations. At one time it was believed that this vacuum or coherent-state noise could not be eliminated.
Recently a number of laboratories have demonstrated the generation of squeezed light, a new kind of light which in some of its aspects exhibits less quantum noise then coherent light. Here a description will be given of how such light is generated and detected. With the successful generation and detection of squeezed light by a number of laboratories1-5 a new degree of control over the quantum statistics of light has been achieved. Light can now be generated which, in some of its aspects, has less quantum noise than coherent light. Such light may find applications in optical communications and in sensitive and precision measurement. Here a description will be given of how squeezed light is generated and detected.6-8 The discussion will be restricted to what is called "quadrature squeezing". The electric field operator for a single mode of the electromagnetic field can be written in the form
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.