Thermal and Quantum Noise in Active Systems

Physical review letters, 2018

There has been significant interest recently in using complex quantum systems to create effective nonreciprocal dynamics. Proposals have been put forward for the realization of artificial magnetic fields for photons and phonons; experimental progress is fast making these proposals a reality. Much work has concentrated on the use of such systems for controlling the flow of signals, e.g., to create isolators or directional amplifiers for optical signals. In this Letter, we build on this work but move in a different direction. We develop the theory of and discuss a potential realization for the controllable flow of thermal noise in quantum systems. We demonstrate theoretically that the unidirectional flow of thermal noise is possible within quantum cascaded systems. Viewing an optomechanical platform as a cascaded system we show here that one can ultimately control the direction of the flow of thermal noise. By appropriately engineering the mechanical resonator, which acts as an artifi...

Thermal noise in mechanical suspension systems is presently the most severe limitation to the sensitivity of the new generation of interferometric gravitational wave detectors, like VIRGO and LIGO, in the frequency range between 5 and 500 Hz. For this reason, a few experimental groups around the world are challenging the strategic goal of queching thermal noise effects.

International Journal of Modern Physics B, 2013

We show through Thermofield Dynamics approach that the action of the thermalized quantum logic gate on the thermalized state is equivalent to thermalization of the state that arise from the application of the nonthermalized quantum logic gate. In particular, we study the effect of temperature on a mixed state associated to a system capable of implementing a controlled-NOT (CNOT) quantum logic gate. According to a proposal in the literature, a way of implementing such a logic gate is by using a representation of the qubit states as elements of the Fock space of a bosonic system. We consider such a proposal and use the Thermofield Dynamics to determine the thermalized qubit states. The temperature acts as a quantum noise on pure states, making them a statistical mixture. In this context, we analyze the fidelity as a function of the temperature and using the Mandel parameter, we determine temperature ranges for which the statistics of the system becomes subpoissonian, poissonian and su...

The observation of quantum phenomena in macroscopic mechanical oscillators has been a subject of interest since the inception of quantum mechanics. It may provide insights into the quantum-classical boundary, experimental investigation of the theory of quantum measurements , the origin of mechanical decoherence [5] and generation of non-classical states of motion.

Foundations of Physics, 2014

In this review article we revisit and spell out the details of previous work on how Berry phase can be used to construct a precision quantum thermometer. An important advantage of such a scheme is that there is no need for the thermometer to acquire thermal equilibrium with the sample. This reduces measurement times and avoids precision limitations. We also review how such methods can be used to detect the Unruh effect. 1 Introduction Introduction.-The science of thermometry is nearly 400 years old, dating back to the work of Galileo, Biancani, Sagredo, and Fludd. It was Ferdinando II de Medici, who constructed the first genuine thermometer, which consisted of sealed tubes with a bulb and stem that were partially filled with alcohol. This device was independent of air pressure, and so the expansion of the liquid within depended only on the temperature of its surrounding environment. Standard commercially available thermometers are precise to approximately 0.01 Celsius degrees. Precision can be considerably improved by using resistance temperature detectors (RTDs). These devices exploit the fact that electrical resistance of platinum responds to temperature in a precisely known way: by 0.00385 ohm per ohm of resistance for each degree C of temperature change. The best such instruments available can resolve temperature differences as small as 10 −7 degrees C. However all such devices require a given substance (alcohol,mercury, platinum) to come into thermal equilibrium with its environment. Here we report on a class of proposed thermometers that make use of quantum effects to determine temperature. These devices make use of temperature-sensitive quantum effects to yield information about temperature. They do not need to come into thermal equilibrium with an environment. Furthermore, they are capable of considerable precision, of order 10 −6 degrees C. The primary quantum-mechanical effect we exploit is the geometric phase. Upon interacting with a quantum field, the state of a point-like quantum system with discrete energy levels (e.g. an atom) acquires a geometric phase [1] that is dependent on the state of the field. If the field is in a thermal state, this geometric phase encodes information about its temperature [2].

European Physical Journal B, 1984

A phenomenological stochastic modelling of the process of thermal and quantal fluctuations of a damped harmonic oscillator is presented. The divergence of the momentum dispersion associated with the Markovian limit is removed by a Drude regularization. The variances of position and momentum are evaluated in closed form at arbitrary temperature and for arbitrary damping. Properties of real and imaginary time correlation functions are discussed, and a spectral decomposition of the equilibrium density matrix is given.

HAL (Le Centre pour la Communication Scientifique Directe), 2002

We describe a new model of massless thermal bosons which predicts an hyperbolic fluctuation spectrum at low frequencies. It is found that the partition function per mode is the Euler generating function for unrestricted partitions p(n). Thermodynamical quantities carry a strong arithmetical structure: they are given by series with Fourier coefficients equal to summatory functions σ k (n) of the power of divisors, with k = −1 for the free energy, k = 0 for the number of particles and k = 1 for the internal energy. Low frequency contributions are calculated using Mellin transform methods. In particular the internal energy per mode diverges asẼ kT = π 2 6x with x = hν kT in contrast to the Planck energyẼ = kT. The theory is applied to calculate corrections in black body radiation and in the Debye solid. Fractional energy fluctuations are found to show a 1/ν power spectrum in the low frequency range. A satisfactory model of frequency fluctuations in a quartz crystal resonator follows. A sketch of the whole Ramanujan-Rademacher theory of partitions is reminded as well.

arXiv (Cornell University), 2017

Although the Fluctuation-Dissipation framework is a first step to get a quantum model for electrical noise, the merging of displacement and conduction currents into the sole current of a series notion like the resistance R(f) does not help in it this task. Used to handle these currents as orthogonal components in electromagnetic waves, the usage of the impedance Z(jf)=R(f)+jX(f) for the noisy device hides the way it interacts with its thermal bath. In contrast to this, the admittance Y(jf) is a parallel notion directly linked with the aforementioned interaction that has led us to develop a discrete model for current fluctuations where single electrons randomly shuttling between any pair of terminals generate the voltage noise we can measure between them.

2013

The quantum measurement problem is revisited and discussed in terms of a new solvable measurement model which basic ingredient is the quantum model of a controlled single-bit memory. The structure of this model involving strongly coupled spin and quantum harmonic oscillator allows to define stable pointer states as well-separated Gaussian states of the quantum oscillator and analyze the transition from quantum to classical regime. The relations between accuracy of measurement, stability of pointer states, effective temperature of joint thermal and quantum noise and minimal work needed to perform the bit-flip are derived. They differ from those based on the Landauer principle and are used to analyze thermodynamic efficiency of quantum Szilard engine and imply more realistic estimations of minimal amount of work needed to perform long computations.

Circuits and Systems, 2012

By a Quantum-compliant model for electrical noise based on Fluctuations and Dissipations of electrical energy in a Complex Admittance, we will explain the phase noise of oscillators that use feedback around L-C resonators. Under this new model that departs markedly from current one based on energy dissipation in Thermal Equilibrium (TE), this dissipation comes from a random series of discrete Dissipations of previous Fluctuations of electrical energy, each linked with a charge noise of one electron in the Capacitance of the resonator. When the resonator out of TE has a voltage between terminals, a discrete Conversion of electrical energy into heat accompanies each Fluctuation to account for Joule effect. This paper shows these Foundations on electrical noise linked with basic skills of electronic Feedback to be used in a subsequent paper where the aforesaid phase noise is explained by the new Admittance-based model for electrical noise.