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Physical Review A

Reply to “Comment on ‘Nonlinear fluctuations and dissipation in matter revealed by quantum light’ ”

Shaul Mukamel, Konstantin E. Dorfman

Published Nov 2, 2015• 0 citations
Publisher

Abstract

We discuss the proper definition of the term ``quantum spectroscopy.'' Since the response of matter to coherent states of the field is not necessarily classical, positivity of the Glauber-Sudarshan $P$ representation as used by Kira et al. [Nat. Phys. 7, 799 (2011)] does not imply that the response is classical. We show that classical and quantum spectroscopies may be unambiguously distinguished by formulating the signals in terms of multipoint field correlation functions.

DOI
10.1103/physreva.92.057802

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In a recent paper [Phys. Rev. A 91, 053844 (2015)], Mukamel and Dorfman compare spectroscopies performed with classical vs quantum light and conclude that nonlinear quantum-spectroscopy signals cannot be obtained from averaging their classical-spectroscopy counterparts over the Glauber-Sudarshan quasiprobability distribution of the quantum field. In this Comment, we show that this interpretation is correct only when classical spectroscopy is perceived as a theoretical description which neglects quantum fluctuations of light altogether. While such an assumption can be a good approximation and useful for comparing theoretical results, it is never realized exactly in laser-spectroscopy experiments that typically use coherent states. Even though coherent states represent the most classical form of light, their quantumness must be considered to fully understand laser-spectroscopy experiments and their connection to quantum spectroscopy, performed with true quantum sources, such as Schr\"odinger's cat states. Thus, instead of using a classical approximation, the connection between coherent states and true quantum states of light must be considered. We rigorously show that quantum spectroscopy can always be projected from the experimentally realized coherent-state spectroscopy regardless how nonlinear the system response is.

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We discuss the proper definition of the term ``quantum spectroscopy.'' Since the response of matter to coherent states of the field is not necessarily classical, positivity of the Glauber-Sudarshan PPP representation as used by Kira et al. [Nat. Phys. 7, 799 (2011)] does not imply that the response is classical. We show that classical and quantum spectroscopies may be unambiguously distinguished by formulating the signals in terms of multipoint field correlation functions.
In a recent paper [Phys. Rev. A 91, 053844 (2015)], Mukamel and Dorfman compare spectroscopies performed with classical vs quantum light and conclude that nonlinear quantum-spectroscopy signals cannot be obtained from averaging their classical-spectroscopy counterparts over the Glauber-Sudarshan quasiprobability distribution of the quantum field. In this Comment, we show that this interpretation is correct only when classical spectroscopy is perceived as a theoretical description which neglects quantum fluctuations of light altogether. While such an assumption can be a good approximation and useful for comparing theoretical results, it is never realized exactly in laser-spectroscopy experiments that typically use coherent states. Even though coherent states represent the most classical form of light, their quantumness must be considered to fully understand laser-spectroscopy experiments and their connection to quantum spectroscopy, performed with true quantum sources, such as Schr\"odinger's cat states. Thus, instead of using a classical approximation, the connection between coherent states and true quantum states of light must be considered. We rigorously show that quantum spectroscopy can always be projected from the experimentally realized coherent-state spectroscopy regardless how nonlinear the system response is.
Quantum optical fields offer numerous control knobs which are not available with classical light and may be used for monitoring the properties of matter by novel types of spectroscopy. It has been recently argued that such quantum spectroscopy signals can be obtained by a simple averaging of their classical spectroscopy counterparts over the Glauber-Sudarshan quasiprobability distribution of the quantum field; the quantum light thus merely provides a novel gating window for the classical response functions. We show that this argument only applies to the linear response and breaks down in the nonlinear regime. The quantum response carries additional valuable information about response and spontaneous fluctuations of matter that may not be retrieved from the classical response by simple data processing. This is connected to the lack of a nonlinear fluctuation-dissipation relation.
In the previous chapters, we have seen that quantum-optical correlations can produce effects that have no classical explanation. In particular, the matter excitations can depend strongly on the specific form of the quantum fluctuations, i.e., the quantum statistics of the light source. For example, Fock-state sources can produce quantum Rabi flopping with discrete frequencies while coherent-state sources generate a sequence of collapses and revivals in atomic excitations. Hence, not only the intensity or the classical amplitude of the field is relevant but also the quantum statistics of the exciting light influences the matter response. Even if we take sources with identical intensities, the resulting atomic excitations are fully periodic for a Fock-state excitation while a coherentstate excitation produces a chaotic Bloch-vector trajectory with multiple collapses and revivals. In this chapter, we use this fundamental observation as the basis to develop the concept of quantum-optical spectroscopy. We show in Chapter 30 that this method yields a particularly intriguing scheme to characterize and control the quantum dynamics in solids. Since one cannot imagine how to exactly compute the many-body wave function or the density matrix, we also study how principal quantum-optical effects can be described with the help of the cluster-expansion scheme. Quantum-optical spectroscopy Historically, the continued refinement of optical spectroscopy and its use to manipulate the states of matter has followed a very distinct path where one simultaneously tries to control and characterize light with increased accuracy.
The classical or quantum nature of optical spectroscopy signals is a topic that has attracted great attention recently. Spectroscopic techniques have been classified as quantum or classical depending on the light-source used in their implementations. In this way, experiments performed with quantum light---such as entangled photon pairs---have been labeled as quantum spectroscopies, whereas those performed with coherent laser pulses are generally referred to as classical ones. In this work, we highlight the fact that typical laser-spectroscopy signals should sometimes be deemed quantum too, as they contain information about the quantum vacua of the modes that interact with the sample. Using a minimalistic model, namely frequency-integrated pump-probe spectroscopy, we demonstrate that vacuum contributions can be expressed as a correction term to the \emph{classical} pump-probe signals, which scales linearly with the intensity of the pump field. Remarkably, we show that these vacuum contributions may not be negligible and lead to the observation of superradiance in pump-probe experiments, provided that fields interacting with the medium are arranged in a collinear configuration.