We study the effect of pure dephasing on the entanglement of a pair of two-level subsystems (qubits). We show that partial dephasing induced by a super-Ohmic reservoir, corresponding to well-established properties of confined charge states and phonons in semiconductors, may lead to complete disentanglement. We show also that the disentanglement effect increases with growing distance between the two subsystems.
We compare disentanglement and decoherence rates within two-spin and three-spin entangled systems subjected to all possible combinations of local and collective pure dephasing noise combinations. In all cases, the bipartite entanglement decay rate is found to be greater than or equal to the dephasing-decoherence rates and often significantly greater. This sharpens previous results for two-spin systems [T. Yu and J. H. Eberly Phys. Rev. B 68, 165322 (2003)] and extends them to the three-spin context.
We relate disentanglement and decoherence rates in a pair of three-level atoms subjected to multi-local and collective pure dephasing noise acting in a preferred basis. The bipartite entanglement decay rate, as bounded from above by the negativity, is found to be greater than or equal to the dephasing-decoherence rates characterized by the decay of off-diagonal elements in the corresponding full density matrix describing the system or the reduced density matrix describing either qutrit, extending previous results for qubit pairs subject to such noise.
We consider whether quantum coherence in the form of mutual entanglement between a pair of qubits is susceptible to decay that may be more rapid than the decay of the coherence of either qubit individually. An instance of potential importance for solid state quantum computing arises if embedded qubits (spins, quantum dots, Cooper pair boxes, etc.) are exposed to global and local noise at the same time. Here we allow separate phase-noisy channels to affect local and non-local measures of system coherence. We find that the time for decay of the qubit entanglement can be significantly shorter tha…
For a wide range of nonclassical magnonic states that have been proposed and demonstrated recently, a new time scale besides the magnon lifetime - the magnon dephasing time - becomes important, but this time scale is rarely studied. Considering exchange interaction and spin-phonon coupling, we evaluate the pure magnon dephasing time and find it to be smaller than the magnon lifetime at temperatures of a few Kelvins. By examining a magnonic cat state as an example, we show how pure dephasing of magnons destroys and limits the survival of quantum superpositions. Thus it will be critical to perfo…
We discuss disentanglement of pure bipartite quantum states within the framework of the schemes developed for entanglement splitting and broadcasting of entanglement.
A general formalism to describe the dynamics of quantum emitters in structured reservoirs is introduced. As an application, we investigate the optical coherence of an atom-like emitter diagonally coupled via a link-boson to a structured bosonic reservoir and obtain unconventional dephasing dynamics due to non-Markovian quantum feedback for different temperatures. For a two-level emitter embedded in a phonon cavity preservation of finite coherence is predicted up to room temperature.
The optimal $N$-pulse dynamical decoupling discovered by Uhrig for a spin-boson mmodel [Phys. Rev. Lett, {\bf 98}, 100504 (2007)] is proved to be universal in suppressing to $O(T^{N+1})$ the pure dephasing or the longitudinal relaxation of a qubit (or spin-1/2) coupled to a generic bath in a short-time evolution of duration $T$. It is also found that for the purpose of suppressing the longitudinal relaxation, an ideal Uhrig $π$-pulse sequence can be generalized to a sequence consisting of the ideal one superimposed with finite-duration pulses satisfying certain symmetry requirements.
Pure dephasing is widely used in the literature to explain experimental observations on quantum dots in cavities. In many cases, its use is not enough and extra terms need to be "fictitiously" added to accomplish with the observed data as it is the case of cavity pumping of an unknown source. Here we controvert the validity of the pure dephasing mechanism as a source of decoherence and present a theoretical study based on the phonon-mediated coupling that can explain the emission spectrum and photon auto- and cross-correlation results in recent experiments without the need of any artificial as…
We demonstrate the emission of highly indistinguishable photons from a quasi-resonantly pumped coupled quantum dot--microcavity system operating in the regime of cavity quantum electrodynamics. Changing the sample temperature allows us to vary the quantum dot--cavity detuning, and on spectral resonance we observe a three-fold improvement in the Hong--Ou--Mandel interference visibility, reaching values in excess of 80\%. Our measurements off-resonance allow us to investigate varying Purcell enhancements, and to probe the dephasing environment at different temperatures and energy scales. By comp…
We consider qubits in a linear arrangement coupled to a bosonic field which acts as a quantum heat bath and causes decoherence. By taking the spatial separation of the qubits explicitly into account, the reduced qubit dynamics acquires an additional non-Markovian element. We investigate the time evolution of an entangled many-qubit W state, which for vanishing qubit separation remains robust under pure dephasing. For finite separation, by contrast, the dynamics is no longer decoherence-free. On the other hand, spatial noise correlations may prevent a complete dephasing. While a standard Bloch-…
We present a tradeoff between leakage and pure dephasing errors for the fluxonium circuit. We show that in the insulating regime, i.e., when the persistent current flowing across the circuit is suppressed, the pure dephasing rate decreases exponentially as the impedance of the circuit is increased. In contrast to this exponential decrease, the qubit remains sufficiently anharmonic so that gates times can still be short, allowing for significant reduction in the computational error rates.
We calculate the two-qubit disentanglement due to classical random telegraph noise using the quasi-Hamiltonian method. This allows us to obtain analytical results even for strong coupling and mixed noise, important when the qubits have tunable working point. We determine when entanglement sudden death and revival occur as functions of qubit working point, noise coupling strength and initial state entanglement. For extended Werner states, we show that the concurrence is related to the difference of two functions: one is related to dephasing and the other longitudinal relaxation. A physical inte…
The filter function formalism quantitatively describes the dephasing of a qubit by a bath that causes Gaussian fluctuations in the qubit energies with an arbitrary noise power spectrum. Here, we extend this formalism to account for more general types of noise that couple to the qubit through terms that do not commute with the qubit's bare Hamiltonian. Our approach applies to any power spectrum that generates slow noise fluctuations in the qubit's evolution. We demonstrate our formalism in the case of singlet-triplet qubits subject to both quasistatic nuclear noise and $1/ω^α$ charge noise and …
We study the dephasing of two-electron states in a single quantum dot in both GaAs and Si. We investigate dephasing induced by electron-phonon coupling and by charge noise analytically for pure orbital excitations in GaAs and Si, as well as for pure valley excitations in Si. In GaAs, polar optical phonons give rise to the most important contribution, leading to a typical dephasing rate of ~5.9 GHz. For Si, intervalley optical phonons lead to a typical dephasing rate of ~140 kHz for orbital excitations and ~1.1 MHz for valley excitations. For harmonic, disorder-free quantum dots, charge noise i…
Understanding decoherence processes is crucial in the study of open quantum systems. In this paper, we discuss the mechanism of pure-dephasing process with a newly proposed boson-boson model, namely, a bosonic field coupled to another bosonic bath in thermal equilibrium. Our model is fully solvable and can reproduce the pure-dephasing process which is usually described by the well-known spin-boson model, therefore offering a new perspective to understanding decoherence processes in open quantum systems of high dimension. We also show that this model admits a generically non-Markovian dynamics …
In coupled quantum systems pure dephasing mechanisms acting on one constituent of the hybrid system break symmetry and enable optical transitions which are forbidden in the non-coupled system, i.e., the pure dephasing bath opens a cascaded dissipation pathway. Here we show that this mechanism enables single-photon induced parametric down-conversion in an ultrastrongly coupled plasmon-exciton system. Fast pure dephasing of the exciton is shown to support photon pair generation as the dominant energy relaxation pathway.
A pure-dephasing reservoir acting on an individual quantum system induces loss of coherence without energy exchange. When acting on composite quantum systems, dephasing reservoirs can lead to a radically different behavior. Transport of energy between two pure-dephasing markovian reservoirs is predicted in this work. They are connected through a chain of coupled sites. The baths are kept in thermal equilibrium at distinct temperatures. Quantum coherence between sites is generated in the steady-state regime and results in the underlying mechanism sustaining the effect. A quantum model for the r…
We investigate the light-matter interaction of a quantum dot with the electromagnetic field in a lossy microcavity and calculate emission spectra for non-zero detuning and dephasing. It is found that dephasing shifts the intensity of the emission peaks for non-zero detuning. We investigate the characteristics of this intensity shifting effect and offer it as an explanation for the non-vanishing emission peaks at the cavity frequency found in recent experimental work.
We examine the phenomenon of {\it entanglement sudden death} (ESD) for $(2 \times 3)$-dimensional systems. As for $2 \times 2$ systems, the negativity vanishes in finite time for some entangled pure as well as mixed states. While locally equivalent pure states do so asymptotically. Interference between the decay of the two upper levels to the lowest one in the qutrit adds further richness to ESD in this systems.
One of the central problems in quantum theory is to characterize, detect, and quantify quantumness in terms of classical strategies. Dephasing processes, caused by non-dissipative information exchange between quantum systems and environments, provides a natural platform for this purpose, as they control the quantum-to-classical transition. Recently, it has been shown that dephasing dynamics itself can exhibit (non)classical traits, depending on the nature of the system-environment correlations and the related (im)possibility to simulate these dynamics with Hamiltonian ensembles---the classical…
We propose a scheme for the detection of qubit-environment entanglement at time $τ$ which requires only operations and measurements on the qubit, all within reach of current experimental state-of-the-art. The scheme works for any type of interaction which leads to pure dephasing of the qubit as long as the initial qubit state is pure. It becomes particularly simple when one of the qubit states is neutral with respect to the environment, such as in case of the most common choice of the NV center spin qubit or for excitonic charge qubits, when the environment is initially at thermal equilibrium.
We investigate the properties of a single photon generated by a solid-state emitter subject to strong pure dephasing. We employ a model in which all the elements of the system, including the propagating fields, are treated quantum mechanically. We analytically derive the density matrix of the emitted photon, which contains full information about the photon, such as its pulse profile, power spectrum, and purity. We visualize these analytical results using realistic parameters and reveal the conditions for maximizing the purity of generated photons.
The influence of pure dephasing on the dynamics of the coupling between a two-level atom and a cavity mode is systematically addressed. We have derived an effective atom-cavity coupling rate that is shown to be a key parameter in the physics of the problem, allowing to generalize the known expression for the Purcell factor to the case of broad emitters, and to define strategies to optimize the performances of broad emitters-based single photon sources. Moreover, pure dephasing is shown to be able to restore lasing in presence of detuning, a further demonstration that decoherence can be seen as…
We propose a qubit-environment entanglement measure which is tailored for evolutions that lead to pure dephasing of the qubit, such as are abundant in solid state scenarios. The measure can be calculated directly form the density matrix without minimization of any kind. In fact it does not require the knowledge of the full density matrix, and it is enough to know the initial qubit state and the states of the environment conditional on qubit pointer states. This yields a computational advantage over standard entanglement measures, which becomes large when there are no correlations between envir…
We present an open-loop unitary strategy to control the coherence in a pure dephasing model (related to the phase-flip channel) that is able to recover, for whatever prescribed time span, the initial coherence at the end of the control process. The strategy's key idea is to steer the quantum state to the subset of invariant states and keep it there the necessary time, using a fine tuned control Hamiltonian.
Analysis of Superradiance-Based Quantum Metrology under Independent Markovian Pure Dephasing
School of Fundamental Science and Technology, Keio University（庆应义塾大学基础理工学部）；Department of Electrical, Electronic, and Communication Engineering, Faculty of Advanced Science and Engineering, Chuo University（中央大学理工学府电气电子通信工程系）；Department of Physics, Simon Fraser University（西蒙菲莎大学物理系）；Center for Spintronics Research Network, Keio University（庆应义塾大学自旋电子学研究网络中心）
We have computed the spectrum emitted spontaneously by a quantum dot coupled to an arbitrarily detuned single mode cavity, taking into account pure dephasing processes. We show that if the emitter is incoherent, the cavity can efficiently emit photons with its own spectral characteristics. This effect opens unique opportunities for the development of devices exploiting both cavity quantum electrodynamics effects and pure dephasing, such as wavelength stabilized single photon sources robust against spectral diffusion.
The interplay between thermal machines and quantum correlations is of great interest in both quantum thermodynamics and quantum information science. Recently, a quantum Szilárd engine has been proposed, showing that the quantum steerability between a Maxwell's demon and a work medium can be beneficial to a work extraction task. Nevertheless, this type of quantum-fueled machine is usually fragile in the presence of decoherence effects. We provide an example of the pure dephasing process, showing that the engine's quantumness can be degraded. Therefore, in this work, we tackle this question by i…
Schroedinger's disentanglement [E. Schroedinger, Proc. Cambridge Phil. Soc. 31, 555 (1935)], i. e., remote state decomposition, as a physical way to study entanglement, is carried one step further with respect to previous work in investigating the qualitative side of entanglement in any bipartite state vector. Remote measurement (or, equivalently, remote orthogonal state decomposition) from previous work is generalized to remote linearly-independent complete state decomposition both in the non-selective and the selective versions. The results are displayed in terms of commutative square diagra…
General semiclassical expression for quantum fidelity (Loschmidt echo) of arbitrary pure and mixed states is derived. It expresses fidelity as an interference sum of dephasing trajectories weighed by the Wigner function of the initial state, and does not require that the initial state be localized in position or momentum. This general dephasing representation is special in that, counterintuitively, all of fidelity decay is due to dephasing and none due to the decay of classical overlaps. Surprising accuracy of the approximation is justified by invoking the shadowing theorem: twice--both for ph…
We study entanglement generated between a charge qubit and a bosonic bath due to their joint evolution which leads to pure dephasing of the qubit. We tune the parameters of the interaction, so that the decoherence is quantitatively independent of the number of bosonic modes taken into account and investigate, how the entanglement generated depends on the size of the environment. A second parameter of interest is the mixedness of the initial state of the environment which is controlled by temperature. We show analytically that for a pure initial state of the environment, entanglement does not d…
An evolution between a system and its environment which leads to pure dephasing of the system may either be a result of entanglement building up between the system and the environment or not (the second option is only possible for initially mixed environmental states). We find a way of distinguishing between an entangling and non-entangling evolutions for systems which are larger than a single qubit. The generalization of the single qubit separability criterion to larger systems is not sufficient to make this distinction (it constitutes a necessary condition of separability). A set of addition…
We show that under the influence of pure vacuum noise two entangled qubits become completely disentangled in a finite time, and in a specific example we find the time to be given by $\ln \Big(\frac{2 +\sqrt 2}{2}\Big)$ times the usual spontaneous lifetime.
We study the relation between the emergence of objectivity and qubit-environment entanglement generation. We find that although entanglement with the unobserved environments is irrelevant (since sufficiently strong decoherence can occur regardless), entanglement with the observed environments is crucial. In fact, the appearance of an objective qubit-observed-environment state is strictly impossible if their joint evolution does not lead to entanglement. Furthermore, if a single observer has access to a single environment (no macrofractions) then the required orthogonality of the observed envir…
In this paper, the dynamical behaviour of the geometric discord of a system consisting of a two-level atom interacting with a quantised radiation field described by the Jaynes-Cummings model has been studied. The evolution of the system has been considered in the pure dephasing regime when the field is initially in a general pure state and the atom is initially in a mixed state. Dynamics of the geometric discord, as a measure of non-classical correlation, has been compared with the dynamics of negativity, as a measure of quantum entanglement. In particular, the influence of different parameter…
Beyond the Purcell Effect: Controlling Pure Quantum Dephasing with Spin Noise Metasurfaces
Elmore Family School of Electrical and Computer Engineering, Purdue University（普渡大学埃尔莫电气与计算机工程学院）；Birck Nanotechnology Center, Purdue University（普渡大学伯里克纳米技术中心）
We consider the coupling of a qubit in a pure state to an environment in an arbitrary state, and characterize the possibility of qubit-environment entanglement generation during the evolution of the joint system, that leads to pure dephasing of the qubit. We give a simple necessary and sufficient condition on the initial density matrix of the environment together with the properties of the interaction, for appearance of qubit-environment entanglement. Any entanglement created turns out to be detectable by the Peres-Horodecki criterion. Furthermore, we show that for a large family of initial en…
We study the effect of a noisy environment on spin and charge transport in ballistic quantum wires with spin-orbit coupling (Rashba coupling). We find that the wire then acts as a ``dephasing diode'', inducing very different dephasing of the spins of right and left movers. We also show how Berry phase (geometric phase) in a curved wire can induce such asymmetric dephasing, in addition to purely geometric dephasing. We propose ways to measure these effects through spin detectors, spin-echo techniques, and Aharanov-Bohm interferometry.
Quantum probing is the art of exploiting simple quantum systems interacting with a complex environment to extract precise information about some environmental parameters, e.g. the temperature of the environment or its spectral density. Here we analyze the performance of a single-qubit probe in characterizing Ohmic bosonic environments at thermal equilibrium. In particular, we analyze the effects of tuning the interaction Hamiltonian between the probe and the environment, going beyond the traditional paradigm of pure dephasing. In the weak-coupling and short-time regime, we address the dynamics…
We study analytically the non-Markovianity of a spin ensemble, with arbitrary number of spins and spin quantum number, undergoing a pure dephasing dynamics. The system is considered as a part of a larger spin ensemble of any geometry with pairwise interactions. We derive exact formulas for the reduced dynamics of the system and for its non-Markovianity as assessed by the witness of Lorenzo \emph{et al.} [Phys.~Rev.~A \textbf{88}, 020102(R) (2013)]. The non-Markovianity is further investigated in the thermodynamic limit when the environment's size goes to infinity. In this limit and for finite-…
We have developed a full quantum microscopic theory to analyze the time evolution of transversal and longitudinal components of an exciton-single photon system coupled to bulk acoustic phonons. These components are subjected to two decay processes. One is radiative relaxation and the other is pure-dephasing due to exciton-phonon interaction. The former results in a decay with an exponent linear to time, while the latter causes a faster initial decay than the radiative decay. We analyzed the dependence of the components on the duration of the input one-photon pulse, temperature, and radiative r…
We investigate pure dephasing decoherence (free induction decay and spin echo) of a spin qubit interacting with a nuclear spin bath. While for infinite magnetic field B the only decoherence mechanism is spectral diffusion due to dipolar flip-flops of nuclear spins, with decreasing B the hyperfine-mediated interactions between the nuclear spins become important. We give a theory of decoherence due to these interactions which takes advantage of their long-range nature. For a thermal uncorrelated bath we show that our theory is applicable down to B~10 mT, allowing for comparison with recent exper…
For many types of superconducting qubits, magnetic flux noise is a source of pure dephasing. Measurements on a representative dc superconducting quantum interference device (SQUID) over a range of temperatures show that $S_Φ(f) = A^2/(f/1 \hbox{Hz})^α$, where $S_Φ$ is the flux noise spectral density, $A$ is of the order of 1 $μΦ_0 \, \hbox{Hz}^{-1/2}$ and $0.61 \leq α\leq 0.95$; $Φ_{0}$ is the flux quantum. For a qubit with an energy level splitting linearly coupled to the applied flux, calculations of the dependence of the pure dephasing time $τ_ϕ$ of Ramsey and echo pulse sequences on $α$ fo…
We study the dynamical process of disentanglement of two qubits and two qutrits coupled to an Ising spin chain in a transverse field, which exhibits a quantum phase transition. We use the concurrence and negativity to quantify entanglement of two qubits and two qutrits, respectively. Explicit connections between the concurrence (negativity) and the decoherence factors are given for two initial states, the pure maximally entangled state and the mixed Werner state. We find that the concurrence and negativity decay exponentially with fourth power of time in the vicinity of critical point of the e…
Thouless's quantum adiabatic pumping is of fundamental interest to condensed-matter physics. It originally considered a zero-temperature equilibrium state uniformly occupying all the bands below a Fermi surface. In the light of recent direct simulations of Thouless's concept in cold-atom systems, this work investigates the dynamics of quantum adiabatic pumping subject to dephasing, for rather general initial states with nonuniform populations and possibly interband coherence. Using a theory based on pure-dephasing Lindblad evolution, we find that the pumping is contributed by two parts of diff…
We find that when a qubit initialized in a pure state experiences pure dephasing due to interaction with an environment, separable qubit-environment states generated during the evolution also have zero quantum discord with respect to the environment. What follows is that the set of separable states which can be reached during the evolution has zero volume and hence, such effects as sudden death of qubit-environment entanglement are very unlikely. In case of the discord with respect to the qubit, a vast majority of separable states qubit-environment is discordant, but in specific situations zer…
