Quantum fluctuations in condensed matter systems: Squeezed states in phonons and Josephson junctions.

Xuedong Hu

Published Jan 1, 1996• 3 citations

Abstract

Quantum fluctuations are an important feature of isolated systems at low temperatures. This quantum noise is unavoidable due to Heisenberg's uncertainty principle. However, squeezed states can lower the quantum noise in one of a pair of variables at the expense of increasing it in the other variable. This ability to reduce quantum fluctuations makes squeezed states very promising in high-precision measurements. This thesis studies the quantum fluctuation properties of two condensed matter systems: phonons and Josephson junctions. In particular, we theoretically investigate several approaches for the generation and detection of squeezed states in these systems. We study for the first time coherent and squeezed quantum states of phonons, in analogy to the coherent and squeezed states of photons. We introduce and study a lattice amplitude operator, which is the phonon analog of the electric field. Our work provides a clear link between quantum mechanical phonon coherent states and the experimentally observed coherent phonons--typically described in classical terms. We then study phonon squeezed states, which can modulate the quantum fluctuations of atomic displacements below the zero-point quantum noise level. We explore the possibility of generating squeezed phonon states with a variety of different approaches, such as a phonon parametric down-conversion process and a polariton-based mechanism. Furthermore, we propose a possible detection scheme based on reflectivity measurements. We also study quantum fluctuation properties of superconducting Josephson junctions, which have the nonlinear interactions necessary for modulating quantum noise. We obtain approximate ground and excited states, and calculate the variances of the charge and phase in various circuit configurations. This thesis provides a first systematic study of quantum noise and its suppression in condensed matter systems. It also proposes different directions for future studies in the control of quantum noise in solids.

Related papers

Squeezed Phonon States: Modulating Quantum Fluctuations of Atomic Displacements

Xuedong Hu, Franco Nori

We study squeezed quantum states of phonons, which allow the possibility of modulating the quantum fluctuations of atomic displacements below the zero-point quantum noise level of coherent phonon states. We calculate the corresponding expectation values and fluctuations of both the atomic displacement and lattice amplitude operators, and also investigate the possibility of generating squeezed phonon states using a three-phonon parametric amplification process based on phonon-phonon interactions. Furthermore, we also propose a detection scheme based on reflectivity measurements.

arXiv:cond-mat/9609188Physical Review LettersMar 25, 1996118 citations

Quantum phonon optics: Coherent and squeezed atomic displacements

Xuedong Hu, Franco Nori

We investigate coherent and squeezed quantum states of phonons. The latter allow the possibility of modulating the quantum fluctuations of atomic displacements below the zero-point quantum noise level of coherent states. The expectation values and quantum fluctuations of both the atomic displacement and the lattice amplitude operators are calculated in these states---in some cases analytically. We also study the possibility of squeezing quantum noise in the atomic displacement using a polariton-based approach. \textcopyright{} 1996 The American Physical Society.

arXiv:cond-mat/9609223Physical review. B, Condensed matterFeb 1, 199676 citations

Phonon Squeezed States Generated by Second-Order Raman Scattering

Xuedong Hu, Franco Nori

We study squeezed states of phonons, which allow a reduction in the quantum fluctuations of the atomic displacements to below the zero-point quantum noise level of coherent phonon states. We investigate the generation of squeezed phonon states using a second-order Raman scattering process. We calculate the expectation values and fluctuations of both the atomic displacement and the lattice amplitude operators, as well as the effects of the phonon squeezed states on macroscopically measurable quantities, such as changes in the dielectric constant. These results are compared with recent experiments.

arXiv:cond-mat/9712078Physical Review LettersDec 8, 199796 citations

Quantum fluctuations and transport in mesoscopic physics

Teemu Ojanen

Mesoscopic physics and nanoelectronics concentrate on systems with dimensions somewhere between atomic and everyday macroscopic scale. Modern technology enables construction of submicron nanostructures where modeling based on classical physics has proven inadequate. It is possible to design electric circuits where dynamics of single electrons and photons are controlled using state-of-the-art experimental methods. For quantitative understanding of these systems it is necessary to resort to a quantum-mechanical description. Quantum phenomena, such as tunneling and a wave-like interference of particles, are essential ingredients of physics in mesoscopic systems. Field of mesoscopic physics contains a rich variety of topics ranging from fundamental condensed matter physics to quantum information processing and possible future technological applications. \n \nThis thesis presents theoretical studies of mesoscopic quantum phenomena in nanostructures and small electronic devices. We have focused on effects of environment fluctuations and investigated connections between fluctuations and transport phenomena. Decoherence in quantum bits (qubits) and quantum state engineering in superconducting circuits are also studied. The theoretical analysis in each case requires an open-system treatment. \n \nEffects of current fluctuations on quantum probe systems have been studied in detail. We have calculated transitions induced by current noise and discussed how these could be used for characterization of fluctuations. We have also shown that electric fluctuations play a key role in radiation and photon heat transport in nanostructures. Motivated by recent advances in mesoscopic electron-photon systems, we have studied a response of a coupled resonator-qubit system, squeezing of quantum fluctuations in small superconducting circuits and investigated decoherence in Josephson flux qubits.

Nov 30, 20070 citations

Superconducting Circuits for Quantum Metrology with Nonclassical Light

Andrew Eddins

The laws of quantum mechanics imply the existence of an intrinsic uncertainty, or noise, in the electromagnetic field. These noise fluctuations are central to many processes in atomic physics and quantum optics, including spontaneous emission of radiation by an atomic system, backaction on an atomic system during non-demolition measurement by probe light, and intrinsic bounds on the noise performance of an ideal amplifier. While quantum noise cannot be eliminated, the noise of one observable quantity may be reduced provided that of the conjugate observable is increased in accord with the relevant Heisenberg uncertainty relation; this process is known as squeezing.Recently, superconducting circuits have emerged as a powerful platform for studying the interaction of squeezed light and matter, leveraging the low-dimensionality of the circuit environment to efficiently couple atomic systems to squeezed radiation. Beyond enabling the verification of canonical predictions of quantum optics, these experiments explore the potential utility of squeezing for the state readout of quantum bits, or qubits, used for quantum information processing.In this thesis, we present three experiments probing the interaction of a superconducting qubit with squeezed radiation. First, we observe how the fluorescence spectra emitted by a two-level atomic system are modified by squeezing of a resonant drive. The subnatural linewidths of the resulting spectra provide the first successful verification in any system of predictions from nearly three decades prior, and provide a tool for characterization of microwave squeezed states. Second, we combine injected squeezed noise with a stroboscopic measurement scheme to demonstrate the first improvement of the signal-to-noise ratio of qubit state readout due to input squeezing. This study includes a characterization of the effect of squeezing on measurement backaction, exhibiting the first use of squeezing to slow measurement-induced dephasing. Finally, we develop a circuit incorporating the qubit inside of a squeezed-microwave source and extensively study the measurement physics of this hybrid system. This device enables the transfer of quantum information from the qubit at $\\sim$30 milliKelvin to a room temperature detector with a marked increase in steady-state efficiency.

Jan 1, 20172 citations

Mekaanisen liikkeen mittauksia ja sovelluksia kvanttimekaanisella rajalla

Erno Damskägg

Microscopic systems exhibit many intriguing quantum mechanical phenomena which cannot be explained by classical physics. Quantum mechanics has succesfully explained the behaviour of subatomic particles, atoms, and electromagnetic waves where entanglement, wave-particle duality and superposition of particles has been observed. In macroscopic scales, quantum mechanics explains the microscopic origin of electronic properties of solids, and quantum coherence effects are routinely observed in superfluids and superconductors. However, most macroscopic objects behave according to the laws of classical physics due to decoherence effects caused by interaction with the environment. Mechanical systems are ideal for studying quantum behavior of macroscopic objects as they can be measured with high accuracy, and their interaction with the environment can be controlled. Cavity optomechanics studies the interaction between light and mechanical objects through radiation pressure force. Recent developments in the field have made it possible to study quantum behaviour in macroscopic mechanical objects. For example, mechanical oscillators coupled to either microwave or optical light have been cooled to their quantum ground state. This thesis studies a cavity optomechanical system in which micromechanical aluminium membrane resonator is coupled to a superconducting microwave circuit resonator. This work focuses on the phenomena relating to the Heisenberg's uncertainty principle which sets a fundamental limit to the precision in which certain pairs of properties of a system can be measured. Due to uncertainty principle, even if a harmonic oscillator is cooled to the ground state, it still has random motion called the zero-point motion. This sets a fundamental limit on how accurately one can measure the motion of the resonator. In a squeezed quantum state, fluctuations of a quantity can be reduced below this quantum limit, at the cost of increased fluctuations in the pair variable. In this work, motion of a nearly macroscopic object is measured in a squeezed state. Due to uncertainty principle, a measurement amplifying an oscillatory signal always adds noise. However, when information in one part of the signal is lost, one can amplify and measure the other part perfectly. This kind of nearly noiseless phase-sensitive measurement, and squeezing of microwave fields is demonstrated in this work. An optomechanical device that simultaneously performs high-gain amplification and frequency conversion is created. Collective dynamics of a multimode optomechanical system is studied. When measuring the oscillator position continuously, the system is perturbed by the measuring. This can be avoided in quantum back-action evading measurement, which is demonstrated for collective motion of two mechanical resonators. Finally, an entanglement of centre-of-mass motion of two nearly macroscopic objects is created and stabilised.

Jan 1, 20180 citations