The gedanken experiment of Maxwell's demon has led to the studies concerning the foundations of thermodynamics and statistical mechanics. The demon measures fluctuations of a system's observable and converts the information gain into work via feedback control. Recent developments have elucidated the relationship between the acquired information and the entropy production and generalized the second law of thermodynamics and the fluctuation theorems. Here we extend the scope to a system subject to quantum fluctuations by exploiting techniques in superconducting circuit quantum electrodynamics. We implement Maxwell's demon equipped with coherent control and quantum nondemolition projective measurements on a superconducting qubit, where we verify the generalized integral fluctuation theorems and demonstrate the information-to-work conversion. This reveals the potential of superconducting circuits as a versatile platform for investigating quantum information thermodynamics under feedback control, which is closely linked to quantum error correction for computation and metrology.
We present an autonomous Maxwell's demon scheme. It is first analysed theoretically in term of information exchange in a closed system and then implemented experimentally with a single Rydberg atom and a high-quality microwave resonator. The atom simulates both a qubit interacting with the cavity, and a demon carrying information on the qubit state. While the cold qubit crosses the hot cavity, the demon prevents energy absorption from the cavity mode, apparently violating the second law of thermodynamics. Taking into account the change of the mutual information between the demon and the qubit-…
It is generally assumed that the vacuum state is the quantum state with the lowest energy. However, it has been shown that this is not the case for a Dirac-Maxwell field in the temporal gauge. In this paper we will present another proof, different from that presented in previous work, which shows that the vacuum state is not the minimum energy state for a Dirac-Maxwell field in the temporal gauge.
We present a novel method for detecting nonlinearities, due to quantum electrodynamics through photon-photon scattering, in Maxwell's equation. The photon-photon scattering gives rise to self-interaction terms, which are similar to the nonlinearities due to the polarisation in nonlinear optics. These self-interaction terms vanish in the limit of parallel propagating waves, but if instead of parallel propagating waves the modes generated in wavesguides are used, there will be a non-zero total effect. Based on this idea, we calculate the nonlinear excitation of new modes and estimate the strengt…
In this paper, operator gauge transformation, first introduced by Kobe, is applied to Maxwell's equations and continuity equation in QED. The gauge invariance is satisfied after quantization of electromagnetic fields. Inherent nonlinearity in Maxwell's equations is obtained as a direct result due to the nonlinearity of the operator gauge transformations. The operator gauge invariant Maxwell's equations and corresponding charge conservation are obtained by defining the generalized derivatives of the first and second kinds. Conservation laws for the real and virtual charges are obtained too. The…
The phenomenological Maxwell field is quantized for arbitrarily space- and frequency-dependent complex permittivity. The formalism takes account of the Kramers--Kronig relation and the dissipation-fluctuation theorem and yields the fundamental equal-time commutation relations of QED. Applications to the quantum-state transformation at absorbing and amplifying four-port devices and to the spontaneous decay of an excited atom in the presence of absorbing dielectric bodies are discussed.
In the standard theory of cavity quantum electrodynamics (QED), coupling between photons inside and outside a cavity (cavity system and photonic reservoir) is given conserving the total number of photons. However, when the cavity photons (ultra)strongly interact with atoms or excitations in matters, the system-reservoir coupling must be determined from a more fundamental viewpoint. Based on the Maxwell's boundary conditions in the QED theory for dielectric media, we derive the quantum Langevin equation and input-output relation, in which the total number of polaritons (not photons) inside the …
A simple algebraic procedure is described for deriving Maxwell-Bloch-type equations from single-atom cavity quantum electrodynamics (cavity QED) master equations via orthogonal projection onto a manifold of semiclassical states. In particular the usual Maxwell-Bloch Equations are obtained--up to a state-dependent correction factor of order unity--straightforwardly from the unconditional Jaynes-Cummings master equation. The technique of projecting onto a semiclassical manifold can also be applied with conditional master equations (quantum filters), leading to stochastic simulation models that i…
Magnetized neutron stars constitute a special class of compact objects harbouring gravitational fields that deviate strongly from the Newtonian weak field limit. Moreover strong electromagnetic fields anchored into the star give rise to non-linear corrections to Maxwell equations described by quantum electrodynamics (QED). Electromagnetic fields close to or above the critical value of $\BQ=4.4\times10^9$~T are probably present in some pulsars and for most of the magnetars. To account properly for emission emanating from the neutron star surface like for instance thermal radiation and its polar…
After giving an outline of the quantization scheme based on the microscopic Hopfield model of a dielectric bulk material, we show how the classical phenomenological Maxwell equations of the electromagnetic field in the presence of dielectric matter of given space- and frequency-dependent complex permittivity can be transferred to quantum theory. Including in the theory the interaction of the medium-assisted field with atomic systems, we present both the minimal-coupling Hamiltonian and the multipolar-coupling Hamiltonian in the Coulomb gauge. To illustrate the concept, we discuss the input--ou…
While quantum measurement theories are built around density matrices and observables, the laws of thermodynamics are based on processes such as are used in heat engines and refrigerators. The study of quantum thermodynamics fuses these two distinct paradigms. In this article, we highlight the usage of quantum process matrices as a unified language for describing thermodynamic processes in the quantum regime. We experimentally demonstrate this in the context of a quantum Maxwell's demon, where two major quantities are commonly investigated; the average work extraction $\langle W \rangle$ and th…
New feasible cavity QED experiment is proposed to analyse reversible quantum decoherence in consequence of quantum complementarity and entanglement. Utilizing the phase selective manipulations with enviroment, it is demonstrated how the complementarity particularly induces a preservation of visibility, whereas quantum decoherence is more progressive due to pronounced entanglement between system and enviroment. This effect can be directly observed using the proposed cavity QED measurements.
The interplay of quantum fluctuations with nonlinear dynamics is a central topic in the study of open quantum systems, connected to fundamental issues (such as decoherence and the quantum-classical transition) and practical applications (such as coherent information processing and the development of mesoscopic sensors/amplifiers). With this context in mind, we here present a computational study of some elementary bifurcations that occur in a driven and damped cavity quantum electrodynamics (cavity QED) model at low intracavity photon number. In particular, we utilize the single-atom cavity QED…
Quantum discord was proposed as an information theoretic measure of the ``quantumness'' of correlations. I show that discord determines the difference between the efficiency of quantum and classical Maxwell's demons in extracting work from collections of correlated quantum systems.
A Maxwell's demon is a device that gets information and trades it in for thermodynamic advantage, in apparent (but not actual) contradiction to the second law of thermodynamics. Quantum-mechanical versions of Maxwell's demon exhibit features that classical versions do not: in particular, a device that gets information about a quantum system disturbs it in the process. In addition, the information produced by quantum measurement acts as an additional source of thermodynamic inefficiency. This paper investigates the properties of quantum-mechanical Maxwell's demons, and proposes experimentally r…
We report the experimental observation, and a theoretical explanation, of collective suppression of linewidths for multiple superconducting qubits coupled to a good cavity. This demonstrates how strong qubit-cavity coupling can significantly modify the dephasing and dissipation processes that might be expected for individual qubits, and can potentially improve coherence times in many-body circuit QED.
We study how correlations affect the performance of the simulator of a Maxwell's demon demonstrated in a recent optical experiment [Vidrighin et al., Phys. Rev. Lett. 116, 050401 (2016)]. The power of the demon is found to be enhanced or hindered, depending on the nature of the correlation, in close analogy to the situation faced by a thermal demon.
Coherent-field QED transitions based on coherent-state boundary conditions
National Institute for Fusion Science, National Institutes of Natural Sciences（日本国立研究开发法人 国立自然科学研究所 核聚变科学研究所）；The Graduate University for Advanced Studies, SOKENDAI（综合研究大学院大学）
The information-theoretic arguments presented in a recent publication on "Quantum discord and Maxwell's demons" are discussed, and found not to address the problem specified by Maxwell. Two interrelated and definitive exorcisms of the demon, one purely thermodynamic, and the other quantum-thermodynamic are briefly discussed. For each of the two exorcisms, the demon is shown to be incapable to accomplish his assignment neither because of limitations arising from information-theoretic tools at his disposal, nor because of the value of his IQ. The limitations are due to the physics of the state o…
An atom placed in a focused laser beam will experience a dipole force due to the gradient in the interaction energy, which is analogous to the well-known optical tweezers effect. This force will be dependent on the velocity of the atom due to the Doppler effect, which could potentially be used to implement a Maxwell's demon. Photon scattering and other forms of dissipation can be negligibly small, which would seem to contradict quantum information proofs that a Maxwell's demon must dissipate a minimum amount of energy. We show that the velocity dependence of the dipole force is cancelled out b…
We present and demonstrate a general three-step method for extracting the quantum efficiency of dispersive qubit readout in circuit QED. We use active depletion of post-measurement photons and optimal integration weight functions on two quadratures to maximize the signal-to-noise ratio of the non-steady-state homodyne measurement. We derive analytically and demonstrate experimentally that the method robustly extracts the quantum efficiency for arbitrary readout conditions in the linear regime. We use the proven method to optimally bias a Josephson traveling-wave parametric amplifier and to qua…
Classical mechanics, relativity, electrodynamics and quantum mechanics are often depicted as separate realms of physics, each with its own formalism and notion. This remains unsatisfactory with respect to the unity of nature and to the necessary number of postulates. We uncover the intrinsic connection of these areas of physics and describe them using a common symplectic Hamiltonian formalism. Our approach is based on a proper distinction between variables and constants, i.e. on a basic but rigorous ontology of time. We link these concept with the obvious conditions for the possibility of meas…
A semiclassical model is presented for characterizing the linear response of elementary quantum optical systems involving cavities, optical fibers, and atoms. Formulating the transmission and reflection spectra using a scattering-wave (transfer matrix) approach, the calculations become easily scalable. To demonstrate how useful this method is, we consider the example of a simple quantum network, i.e., two cavity-QED systems connected via an optical fiber. Differences between our quasi-exact transfer matrix approach and a single-mode, linearized quantum-optical model are demonstrated for parame…
We describe a minimal model of a quantum Maxwell demon obeying Hamiltonian dynamics. The model is solved exactly, and we analyze its steady-state behavior. We find that writing information to a quantum memory induces a probability current through the demon, which is the quantum analog of the classical Maxwell demon's action. Our model offers a simple and pedagogical paradigm for investigating the thermodynamics of quantum information processing.
This paper provides an overview of the first experimental realizations of quantum-mechanical Maxwell's demons based on superconducting circuits. The principal results of these experiments are recalled and put into context. We highlight the versatility offered by superconducting circuits for studying quantum thermodynamics.
The long-standing paradigm of Maxwell's demon is till nowadays a frequently investigated issue, which still provides interesting insights into basic physical questions. Considering a single-electron transistor, where we implement a Maxwell demon by a piecewise-constant feedback protocol, we investigate quantum implications of the Maxwell demon. To this end, we harness a dynamical coarse-graining method, which provides a convenient and accurate description of the system dynamics even for high measurement rates. In doing so, we are able to investigate the Maxwell demon in a quantum-Zeno regime l…
Maxwell's demon was born in 1867 and still thrives in modern physics. He plays important roles in clarifying the connections between two theories: thermodynamics and information. Here, we present the history of the demon and a variety of interesting consequences of the second law of thermodynamics, mainly in quantum mechanics, but also in the theory of gravity. We also highlight some of the recent work that explores the role of information, illuminated by Maxwell's demon, in the arena of quantum information theory.
We demonstrate a universal physical mechanism to probe the macroscopic quantum phase transition based on circuit QED architecture. We found that, with certain parameters, the Josephson junction qubit array behaves as an antiferromagnetic Ising model in transverse field and the coupled transmission line resonator serves as a bosonic quantum probe. Our investigation shows that, at the critical point, the drastic broadening of the spectrum of the probe indicates the quantum phase transition.
This chapter will primarily focus on the studies of quantum optics with semiconductor, epitaxially grown quantum dots embedded in photonic crystal cavities. We will start by giving brief introductions into photonic crystals and quantum dots, then proceed with the introduction to cavity quantum electrodynamics (QED) effects, with a particular emphasis on the demonstration of these effects on the quantum dot-photonic crystal platform. Finally, we will focus on the applications of such cavity QED effects.
