We show that the unitary evolution of a harmonic oscillator coupled to a two-level system can be undone by a suitable manipulation of the two-level system -- more specifically: by a quasi-instantaneous phase change. This enables us to isolate the dissipative evolution to which the oscillator may be exposed in addition. With this method we study the decoherence of a photon mode in cavity QED, and that of the quantized harmonic motion of trapped ions. We comment on the relation to spin echoes and multi-path interferometry.
A system of a particle and a harmonic oscillator, which have pure point spectrum if uncoupled, is known to acquire absolutely continuous spectrum when the particle and the oscillator are coupled by a sufficiently strong point interaction. Here the simple dynamical mechanism underlying this phenomenon is exposed. The energy of the oscillator is proven to exponentially diverge in time, while the spatial probability distribution of the particle collapses into a delta function in the interaction point. On account of this result, a generalized model with many oscillators which interact with the par…
We propose a scheme to measure the quantum state of a nanomechanical oscillator cooled near its ground state of vibrational motion. This is an extension of the nonlinear atomic homodyning technique scheme first developed to measure the intracavity field in a micromaser. It involves the use of a detector-atom that is simultaneously coupled to the cantilever via a magnetic interaction and to (classical) optical fields via a Raman transition. We show that the probability for the atom to be found in the excited state is a direct measure of the Wigner characteristic function of the nanomechanical o…
Nowadays, two of the most prospering fields of physics are quantum computing and spintronics. In both, the loss of information and dissipation plays a crucial role. In the present work we formulate the quantization of the dissipative oscillator, which aids understanding of the above mentioned, and creates a theoretical frame to overcome these issues in the future. Based on the Lagrangian framework of the damped spring system, the canonically conjugated pairs and the Hamiltonian of the system are obtained, by which the quantization procedure can be started and consistently applied. As a result,…
We investigate the possibility of measuring the thermal Casimir force and its gradient in the configuration of a plate and a microfabricated cylinder attached to a micromachined oscillator. The Lifshitz-type formulas in this configuration are derived using the proximity force approximation. The accuracy for the obtained expressions is determined from a comparison with exact results available in ideal metal case. Computations of the thermal correction to both the Casimir force and its gradient are performed in the framework of different theoretical approaches proposed in the literature. The cor…
It is well known that a state with complex energy cannot be the eigenstate of a self-adjoint operator, like the Hamiltonian. Resonances, i.e. states with exponentially decaying observables, are not vectors belonging to the conventional Hilbert space. One can describe these resonances in an unusual mathematical formalism, based on the so-called Rigged Hilbert Space (RHS). In the RHS, the states with complex energy are denoted as Gamow Vectors (GV), and they model decay processes. We study GV of the Reversed Harmonic Oscillator (RHO), and we analytically and numerically investigate the unstable …
The dynamics of a quantum anharmonic oscillator whose position is monitored by a Bose-Einstein condensate (BEC) trapped in a symmetric double well potential is studied. The (non-exponential) decoherence induced on the oscillator by the measuring device is analysed. A detailed quasiclassical and quantum analysis is presented. In the first case, for an arbitrary initial coherent state, two different decoherence regimes are observed: An initial Gaussian decay followed by a power law decay for longer times. The characteristic time scales of both regimes are reported. Analytical approximated expres…
We study theoretically the measurement of a mechanical oscillator using a single two level system as a detector. In a recent experiment, we used a single electronic spin associated with a nitrogen vacancy center in diamond to probe the thermal motion of a magnetized cantilever at room temperature {Kolkowitz et al., Science 335, 1603 (2012)}. Here, we present a detailed analysis of the sensitivity limits of this technique, as well as the possibility to measure the zero point motion of the oscillator. Further, we discuss the issue of measurement backaction in sequential measurements and find tha…
We determine the quantum Cramér-Rao bound for the precision with which the oscillator frequency and damping constant of a damped quantum harmonic oscillator in an arbitrary Gaussian state can be estimated. This goes beyond standard quantum parameter estimation of a single mode Gaussian state for which typically a mode of fixed frequency is assumed. We present a scheme through which the frequency estimation can nevertheless be based on the known results for single-mode quantum parameter estimation with Gaussian states. Based on these results, we investigate the optimal measurement time. For mea…
Thermal-fluctuator driven decoherence of an oscillator resonantly coupled to a two-level system
School of Physics and Astronomy and Centre for the Mathematics and Theoretical Physics of Quantum Non-Equilibrium Systems, University of Nottingham（诺丁汉大学物理与天文学院及量子非平衡系统数学与理论物理中心）
Two measurable characteristics of microwave one-mode photon states are discussed: a rotated quadrature distribution (tomogram) and normally/antinormally ordered moments of photon creation and annihilation operators. Extraction of these characteristics from amplified microwave signal is presented. Relations between the tomogram and the moments are found and can be used as a cross check of experiments. Formalism of the ordered moments is developed. The state purity and generalized uncertainty relations are considered in terms of moments. Unitary and non-unitary time evolution of moments is obtai…
The geometrical Berry phase is key to understanding the behaviour of quantum states under cyclic adiabatic evolution. When generalised to non-Hermitian systems with gain and loss, the Berry phase can become complex, and should modify not only the phase but also the amplitude of the state. Here, we perform the first experimental measurements of the adiabatic non-Hermitian Berry phase, exploring a minimal two-site $\mathcal{PT}$-symmetric Hamiltonian that is inspired by the Hatano-Nelson model. We realise this non-Hermitian model experimentally by mapping its dynamics to that of a pair of classi…
We study theoretically the dynamics of a a hybrid optomechanical system consisting of a macroscopic mechanical membrane magnetically coupled to a spinor Bose-Einstein condensate via a nanomagnet attached at the membrane center. We demonstrate that this coupling permits us to monitor indirectly the center-of-mass position of the membrane via measurements of the spin of the condensed atoms. These measurements normally induce a significant backaction on the membrane motion, which we quantify for the cases of thermal and coherent initial states of the membrane. We discuss the possibility of measur…
We present a way of measuring with high precision the anharmonicity of a quantum oscillator coupled to an optical field via radiation pressure. Our protocol uses a sequence of pulsed interactions to perform a loop in the phase space of the mechanical oscillator, which is prepared in a thermal state. We show how the optical field acquires a phase depending on the anharmonicity. Remarkably, one only needs small initial cooling of the mechanical motion to probe even small anharmonicities. Finally, by applying tools from quantum estimation theory, we calculate the ultimate bound on the estimation …
The Aharonov-Anandan phase is a description of the geometric nature in non-adiabatic cyclic evolutions of quantum states. Here we report on a measurement of the Aharonov-Anandan phase in photonics. We consider a time-independent quantum driven harmonic oscillator that is initially prepared at the vacuum state. We utilize evanescently coupled waveguides to realize this physical model and achieve a measurement of the Aharonov-Anandan phase via integrated interferometry.
Quantum mechanics sets a limit for the precision of continuous measurement of the position of an oscillator. Here we show how it is possible to measure an oscillator without quantum backaction of the measurement by constructing one effective oscillator from two physical oscillators. We realize such a quantum-mechanics free subsystem using two micromechanical oscillators, and show the measurements of two collective quadratures while evading the quantum backaction by $8$ decibels on both of them, obtaining a total noise within a factor two of the full quantum limit. This facilitates detection of…
We measure the state dynamics of a tunable anharmonic quantum system, the Josephson phase circuit, under the excitation of a frequency-chirped drive. At small anharmonicity, the state evolves like a wavepacket - a characteristic response in classical oscillators; in this regime we report exponentially enhanced lifetimes of highly excited states, held by the drive. At large anharmonicity, we observe sharp steps, corresponding to the excitation of discrete energy levels. The continuous transition between the two regimes is mapped by measuring the threshold of these two effects.
The thermodynamic implications for the out-of-equilibrium dynamics of quantum systems are to date largely unexplored, especially for quantum many-body systems. In this paper we investigate the paradigmatic case of an array of nearest-neighbor coupled quantum harmonic oscillators interacting with a thermal bath and subjected to a quench of the inter-oscillator coupling strength. We study the work done on the system and its irreversible counterpart, and characterize analytically the fluctuation relations of the ensuing out-of-equilibrium dynamics. Finally, we showcase an interesting functional l…
We propose a new method to overcome quantum back-action in a measurement process using oscillators. An optical oscillator is used as a meter to measure the parameters of another open oscillator. The optical oscillator is synthesized such that the optical restoring force counters any perturbations induced by the quantum back-action phenomena. As a result, it is shown that the quantum back-action in continuous measurement is suppressed in the low frequency regime i.e., for frequencies much smaller than the resonance frequency of the open oscillator. As the meter plays the role of measuring param…
We present a protocol for measuring the quadrature of a harmonic oscillator (HO). The HO is coupled to a qubit, with an interaction modulated by the qubit control and effectively proportional to the HO quadrature $I$. Repeated measurement of the qubit leads to gradually increasing information on the quadrature $I$, leading to squeezing. We derive an analytical formula for the quadrature variance, $(ΔI)^2 = 1/(1+4ϕ^2 s)$, with $ϕ$ the product of interaction strength and interaction time and $s$ the number of repetitions of the measurement. We discuss the robustness of this scheme against decohe…
Dynamical phases are obtained for a quantum thermal engine, whose working medium is a single harmonic oscillator. The dynamics of this engine is obtained by using four steps where in two steps the time dependent frequency is changing. In the other two steps, the thermal engine is coupled alternatively to hot and cold heat baths. Similar dynamical phases are obtained in a quantum thermal engine whose working medium is spin 1/2 system. The role of times durations of such steps in the quantum engines for getting maximal efficiency is analyzed. The dynamic of charge pumping in a quantum dot couple…
Ultralow dissipation plays an important role in sensing applications and exploring macroscopic quantum phenomena using micro-and nano-mechanical systems. We report a diamagnetic-levitated micro-mechanical oscillator operating at a low temperature of 3K with measured dissipation as low as 0.59 $μ$Hz and a quality factor as high as $2 \times 10^7$. To the best of our knowledge the achieved dissipation is the lowest in micro- and nano-mechanical systems to date, orders of magnitude improvement over the reported state-of-the-art systems based on different principles. The cryogenic diamagnetic-levi…
Superconducting circuits extensively rely on the Josephson junction as a nonlinear electronic element for manipulating quantum information and mediating photon interactions. Despite continuing efforts in designing anharmonic Josephson circuits with improved coherence times, the best photon lifetimes have been demonstrated in microwave cavities. Nevertheless, architectures based on quantum memories need a qubit element for addressing these harmonic modules at the cost of introducing additional loss channels and limiting process fidelities. This work focuses on tailoring the oscillator Hilbert s…
The Heisenberg uncertainty principle sets a lower bound on the sensitivity of continuous optical measurements of force. This bound, the standard quantum limit, can only be reached when a mechanical oscillator subjected to the force is unperturbed by its environment, and when measurement imprecision from photon shot-noise is balanced against disturbance from measurement backaction. We apply an external force to the center-of-mass motion of an ultracold atom cloud in a high-finesse optical cavity. The optomechanically transduced response clearly demonstrates the trade-off between measurement imp…
We show that the recently discovered quantum-enhanced measurement protocol of coherent averaging that is capable of achieving Heisenberg-limited sensitivity without using entanglement, has a classical analogue. The classical protocol uses N harmonic oscillators coupled to a central oscillator and one measures the signal from the latter. We propose an application to the measurement of very weak interactions, and, in particular, a novel route to measuring the gravitational constant with enhanced precision.
In this PhD thesis, we will present the theoretical and experimental work that led to the realization of a radio-frequency circuit quantum electrodynamics system (RFcQED). In chapter 2, we provide a detailed derivation of the Hamiltonian of circuit QED formulated in the context of the Rabi model, and extract expressions for the cross-Kerr interaction. The resulting requirements for the coupling rate in RFcQED are discussed, one of them being the need to dramatically increase the coupling rate compared to typical circuit QED device. In chapter 3 we cover two experimental approaches to increasin…
We consider an optical probe that interacts with an ensemble of rare earth ions doping a materialin the shape of a cantilever. By optical spectral hole burning, the inhomogeneously broadenedtransition in the ions is prepared to transmit the probe field within a narrow window, but bendingof the cantilever causes strain in the material which shifts the ion resonances. The motion of thecantilever may thus be registered by the phase shift of the probe. By continuously measuringthe optical field we induce a rapid reduction of the position and momentum uncertainty of thecantilever. Doing so, the pro…
Cooling the motion of a massive mechanical oscillator into its quantum ground state plays an essential role in observing macroscopic quantum effects in mechanical systems. Here we propose a measurement-based feedback cooling protocol in cavity magnomechanics that is able to cool the mechanical vibration mode of a macroscopic ferromagnet into its ground state. The mechanical mode couples to a magnon mode via a dispersive magnetostrictive interaction, and the latter further couples to a microwave cavity mode via the magnetic-dipole interaction. A feedback loop is introduced by measuring the ampl…
