For an electron spin in coupling with an interacting spin chain via hyperfine-type interaction, we investigate the dynamical evolutions of the pairwise entanglement of the spin chain and a correlation function joined the electron spin with a pair of chain spins in correspondence to the electron spin coherence evolution. Both quantities manifest a periodic and a decaying evolution. The entanglement of the spin bath is significant in distinguishing the zero-coherence status exhibited in periodic and decoherence evolutions of the electron spin. The periodical concurrence evolution of the spin bath characterizes the whole system in a coherence-preserving phase, particularly for the case that the associated periodic coherence evolution is predominated by zero-value in the infinite chain-length limit, which was often regarded as the realization of decoherence.
We demonstrate through exact solutions that a spin bath leads to stronger (faster) dephasing of a qubit than a bosonic bath with identical bath-coupling spectrum. This difference is due to the spin-bath "dressing" by the coupling. Consequently, the quantum statistics of the bath strongly affects the pulse sequences required to dynamically decouple the qubit from its bath.
We introduce an exactly solvable model to study decoherence of a central spin interacting with a spin bath where the coupling is mediated by phonons which we assume to be in a coherent state or thermal distribution. For the coherent state case, we find that the decoherence factor decays in a Gaussian fashion and it becomes independent of the phonon frequencies at short times. If the phonon energies are much larger than spin-phonon coupling or bath spins are fully polarized, decoherence time becomes independent of the initial phonon state. For the thermal state case, phonons play more important…
Decoherence of quantum objects in noisy environments is important in quantum sciences and technologies. It is generally believed that different processes coupled to the same noise source should have similar decoherence behaviors and stronger noises would cause faster decoherence. Here we show that in a quantum bath, the case can be the opposite. In particular, we predict that the multi-transition of a nitrogen-vacancy center spin-1 in diamond can have longer coherence time than the single-transitions, even though the former suffers twice stronger noises from the nuclear spin bath than the latt…
We revisit the problem of the decoherence and relaxation of a central spin coupled to a bath of conduction electrons. We consider both metallic and semiconducting baths to study the effect of a gap in the bath density of states (DOS) on the time evolution of the density matrix of the central spin. We use two weak coupling approximation schemes to study the decoherence. At low temperatures, though the temperature dependence of the decoherence rate in the case of a metallic bath is the same irrespective of the details of the bath, the same is not true for the semiconducting bath. We also calcula…
We theoretically study the decoherence and the dynamical decoupling control of nitrogen-vacancy center electron spins in high-purity diamond, where the hyperfine interaction with $^{13}$C nuclear spins is the dominating decoherence mechanism. The decoherence is formulated as the entanglement between the electron spin and the nuclear spins, which is induced by nuclear spin bath evolution conditioned on the electron spin state. The nuclear spin bath evolution is driven by elementary processes such as single spin precession and pairwise flip-flops. The importance of different elementary processes…
The decoherence of mixed electron-nuclear spin qubits is a topic of great current importance, but understanding is still lacking: while important decoherence mechanisms for spin qubits arise from quantum spin bath environments with slow decay of correlations, the only analytical framework for explaining observed sharp variations of decoherence times with magnetic field is based on the suppression of classical noise. Here we obtain a general expression for decoherence times of the central spin system which exposes significant differences between quantum-bath decoherence and decoherence by class…
Decoherence of a center spin or qubit in a spin bath is essentially determined by the many-body bath evolution. We develop a cluster-correlation expansion (CCE) theory for the spin bath dynamics relevant to the qubit decoherence problem. A cluster correlation term is recursively defined as the evolution of a group of bath spins divided by the cluster correlations of all the subgroups. The so-defined correlation accounts for the authentic collective excitations within a given group. The bath propagator is the product of all possible cluster correlation terms. For a finite-time evolution as in t…
We experimentally demonstrate that the decoherence of a spin by a spin bath can be completely eliminated by fully polarizing the spin bath. We use electron paramagnetic resonance at 240 gigahertz and 8 Tesla to study the spin coherence time $T_2$ of nitrogen-vacancy centers and nitrogen impurities in diamond from room temperature down to 1.3 K. A sharp increase of $T_2$ is observed below the Zeeman energy (11.5 K). The data are well described by a suppression of the flip-flop induced spin bath fluctuations due to thermal spin polarization. $T_2$ saturates at $\sim 250 μs$ below 2 K, where the …
Decoherence of quantum objects is critical to modern quantum sciences and technologies. It is generally believed that stronger noises cause faster decoherence. Strikingly, recent theoretical research discovers the opposite case for spins in quantum baths. Here we report experimental observation of the anomalous decoherence effect for the electron spin-1 of a nitrogen-vacancy centre in high-purity diamond at room temperature. We demonstrate that under dynamical decoupling, the double-transition can have longer coherence time than the single-transition, even though the former couples to the nucl…
We examine the decoherence of an asymmetric two-qubit system that is coupled via a tunable interaction term to a common bath or two individual baths of harmonic oscillators. The dissipative dynamics are evaluated using the Bloch-Redfield formalism. It is shown that the behaviour of the decoherence effects is affected mostly by different symmetries between the qubit operator which is coupled to the environment and temperature, whereas the differences between the two bath configurations are very small. Moreover, it is elaborated that small imperfections of the qubit parameters do not lead to a d…
Decoherence of a central spin coupled to an interacting spin bath via inhomogeneous Heisenberg coupling is studied by two different approaches, namely an exact equations of motion (EOMs) method and a Chebyshev expansion technique (CET). By assuming a wheel topology of the bath spins with uniform nearest-neighbor $XX$-type intrabath coupling, we examine the central spin dynamics with the bath prepared in two different types of bath initial conditions. For fully polarized baths in strong magnetic fields, the polarization dynamics of the central spin exhibits a collapse-revival behavior in the in…
We theoretically investigate spin decoherence of a single nitrogen-vacancy (NV) center in diamond. Using the spin coherent state P-representation method, coherence evolution of the NV center surrounded by nitrogen electron spins (N) is simulated. We find that spin decoherence time as well as free-induction decay of the NV center depend on the spatial configuration of N spins. Both the spin decoherence rate (1/T2) and dephasing rate (1/T2*) of the NV center increase linearly with the concentration of the N spins. Using the P-representation method, we also demonstrate extracting noise spectrum o…
We study an analytically solvable model for decoherence of a two spin system embedded in a large spin environment. As a measure of entanglement, we evaluate the concurrence for the Bell states (Einstein-Podolsky-Rosen pairs). We find that while for two separate spin baths all four Bell states lose their coherence with the same time dependence, for a common spin bath, two of the states decay faster than the others. We explain this difference by the relative orientation of the individual spins in the pair. We also examine how the Bell inequality is violated in the coherent regime. Both for one b…
We develop a "chain-boson model" master equation, within the Born-Markov approximation, for a few superconducting quantum interference devices (SQUIDs) coupled into a chain and exchanging their angular momenta with a low temperature phonon bath. Our master equation has four generators; we concentrate on the damping and diffusion and use them to study the relaxation and decoherence of a Heisenberg SQUID chain whose spectrum exhibits critical point energy-level crossings, entangled states, and pairs of resonant transitions. We note that at an energy-level crossing the relevant bath wavelengths a…
The clock transitions (CTs) of central spins have long coherence times because their frequency fluctuations vanish in the linear order of external field noise (such as Overhauser fields from nuclear spin baths). Therefore, CTs are useful for quantum technologies. Also, the quadratic dependence of frequencies on noises makes the CT decoherence an interesting physics problem. Thus we are motivated to study the decoherence of CTs. We consider noise from spin baths, which is one of the most relevant mechanisms of qubit decoherence. Various quantum many-body methods have been developed to study the…
Many-body correlations can yield key insights into the nature of interacting systems; however, detecting them is often very challenging in many-particle physics, especially in nanoscale systems. Here, taking a phosphorus donor electron spin in a natural-abundance 29Si nuclear spin bath as our model system, we discover both theoretically and experimentally that many-body correlations in nanoscale nuclear spin baths produce identifiable signatures in the decoherence of the central spin under multiple-pulse dynamical decoupling control. We find that when the number of decoupling -pulses is odd, c…
In the framework of nuclear magnetic resonance, we consider the general problem of the coherent control of a spin coupled to a bath by means of composite or continuous pulses of duration $τ_\mathrm{p}$. We show explicity that it is possible to design the pulse in order to achieve a decoupling of the spin from the bath up to the third order in $τ_\mathrm{p}$. The evolution of the system is separated in the evolution of the spin under the action of the pulse and of the bath times correction terms. We derive the correction terms for a general time dependent axis of rotation and for a general coup…
The dynamics of a spin-1/2 particle coupled to a nuclear spin bath through an isotropic Heisenberg interaction is studied, as a model for the spin decoherence in quantum dots. The time-dependent polarization of the central spin is calculated as a function of the bath-spin distribution and the polarizations of the initial bath state. For short times, the polarization of the central spin shows a gaussian decay, and at later times it revives displaying nonmonotonic time dependence. The decoherence time scale dep ends on moments of the bath-spin distribuition, and also on the polarization strength…
In this paper, we explore the decoherence dynamics of a probing spin coupled to a spin bath, where the spin bath is given by a controllable 1D transverse-field Ising chain. The 1D transverse-field Ising chain with free-ends boundary condition is equivalent to a modified Kitaev model with non-local Majorana bound states in its topological phase. We find that the probing spin non-Markovian decoherence dynamics can manifest the topological structure of the spin chain. By controlling the external magnetic field on the Ising chain, we find the close relationships between the quantum phase transitio…
In this paper, we study the electron spin decoherence of single defects in silicon carbide (SiC) nuclear spin bath. We find that, although the natural abundance of $^{29}\rm{Si}$ ($p_{\rm{Si}}=4.7\%$) is about 4 times larger than that of $^{13}{\rm C}$ ($p_{\rm{C}}=1.1\%$), the electron spin coherence time of defect centers in SiC nuclear spin bath in strong magnetic field ($B>300~\rm{Gauss}$) is longer than that of nitrogen-vacancy (NV) centers in $^{13}{\rm C}$ nuclear spin bath in diamond. The reason for this counter-intuitive result is the suppression of heteronuclear-spin flip-flop proces…
A major problem facing the realisation of scalable solid-state quantum computing is that of overcoming decoherence - the process whereby phase information encoded in a qubit is lost as the qubit interacts with its environment. Due to the vast number of environmental degrees of freedom, it is challenging to accurately calculate decoherence times $T_2$, especially when the qubit and environment are highly correlated. Hybrid or mixed electron-nuclear spin qubits, such as donors in silicon, possess 'optimal working points' (OWPs) which are sweet-spots for reduced decoherence in magnetic fields. An…
Decoherence of a center spin or qubit in a spin bath is essentially determined by the many-body bath evolution. The bath dynamics can start either from a pure state or, more generally, from a statistical ensemble. In the preceding article [W. Yang and R. B. Liu, Phys. Rev. B \textbf{78}, 085315 (2008)], we have developed the cluster-correlation expansion (CCE) theory for the so-called single-sample bath dynamics initiated from a factorizable pure state. Here we present the ensemble CCE theory, which is based on similar ideas of the single-sample CCE: The bath evolution is factorized into the p…
Control of electron spin decoherence in contact with a mesoscopic bath of many interacting nuclear spins in an InAs quantum dot is studied by solving the coupled quantum dynamics. The nuclear spin bath, because of its bifurcated evolution predicated on the electron spin up or down state, measures the which-state information of the electron spin and hence diminishes its coherence. The many-body dynamics of nuclear spin bath is solved with a pair-correlation approximation. In the relevant timescale, nuclear pair-wise flip-flops, as elementary excitations in the mesoscopic bath, can be mapped int…
We study the decoherence of a central spin 1/2 induced by a spin bath with intrabath interactions. Since we are interested in the cumulative effect of interaction and disorder, we study baths comprising Ising spins with random ferro- and antiferromagnetic interactions between the spins. Using the resolvent operator method which goes beyond the standard Born-Markov master equation approach, we show that, in the weak coupling regime, the decoherence of the central spin at all times is entirely determined by the local-field distribution or equivalently, the dynamical structure factor of the Ising…
Decoherence of electron spins in nanoscale systems is important to quantum technologies such as quantum information processing and magnetometry. It is also an ideal model problem for studying the crossover between quantum and classical phenomena. At low temperatures or in light-element materials where the spin-orbit coupling is weak, the phonon scattering in nanostructures is less important and the fluctuations of nuclear spins become the dominant decoherence mechanism for electron spins. Since 1950s, semiclassical noise theories have been developed for understanding electron spin decoherence.…
Understanding and mitigating decoherence is a key challenge for quantum science and technology. The main source of decoherence for solid-state spin systems is the uncontrolled spin bath environment. Here, we demonstrate quantum control of a mesoscopic spin bath in diamond at room temperature that is composed of electron spins of substitutional nitrogen impurities. The resulting spin bath dynamics are probed using a single nitrogen-vacancy (NV) centre electron spin as a magnetic field sensor. We exploit the spin bath control to dynamically suppress dephasing of the NV spin by the spin bath. Fur…
We develop a theoretical model for transverse dynamics of a single electron spin interacting with a nuclear spin bath. The approach allows a simple diagrammatic representation and analytical expressions of different nuclear spin excitation processes contributing to electron spin decoherence and dynamical phase fluctuations. It accounts for nuclear spin dynamics beyond conventional pair correlation models. As an illustration of the theory, we evaluated the coherence dynamics of a P donor electron spin in a Si crystal.
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…
We present a technique for treating many particles moving inside a ballistic interferometer, under the influence of a quantum-mechanical environment (phonons, photons, Nyquist noise etc.). Our approach is based on solving the coupled Heisenberg equations of motion of the many-particle system and the bath and is inspired by the quantum Langevin method known for the Caldeira Leggett model. It allows to study decoherence and the influence of the bath on other properties of the interferometer. As a first application, we treat a fermionic Mach-Zehnder interferometer. In particular, we discuss the d…
We study the decoherence of a spin in a quantum dot due to its hyperfine coupling to a randomly fluctuating bath of nuclear spins. The system is modelled by the central spin model with the spin bath initially being at infinite temperature. We calculate the spectrum and time evolution of the coherence factor using a Monte Carlo sampling of the exact eigenstates obtained via the algebraic Bethe ansatz. The exactness of the obtained eigenstates allows us to study the non-perturbative regime of weak magnetic fields in a full quantum mechanical treatment. In particular, we find a large non-decaying…
A simple model is considered for an open system consisting of an aggregation of magnetic particles (like greigite) in the presence of a magnetic field (H), and interacting linearly with a bath of 3D harmonic oscillators. Using the Feynman-Vernon formalism, as given in Weiss (termed FVW), the time-evolved reduced density matrix (after eliminating the bath d.o.f.'s), is examined for environmental decoherence as defined in the FVW formalism. While decoherence is usually positive for most two-way couplings with the enviroment, it is found that a $three-way$ interaction involving the system plus ba…
An exactly solvable model for the decoherence of one and two-qubit states interacting with a spin-bath, in the presence of a time-dependent magnetic field is studied. The magnetic field is static along $\hat{z}$ direction and oscillatory in the transverse plane. The transition probability and Rabi oscillations between the spin-states of a single qubit is shown to depend on the size of bath, the distribution of qubit-bath couplings and the initial bath polarization. In contrast to the fast Gaussian decay for short times, the polarization of the qubit shows an oscillatory power-law decay for lon…
We present pulsed electron-nuclear double resonance (ENDOR) experiments which enable us to characterize the coupling between bismuth donor spin qubits in Si and the surrounding spin bath of 29Si impurities which provides the dominant decoherence mechanism (nuclear spin diffusion) at low temperatures (< 16 K). Decoupling from the spin bath is predicted and cluster correlation expansion simulations show near-complete suppression of spin diffusion, at optimal working points. The suppression takes the form of sharply peaked divergences of the spin diffusion coherence time, in contrast with previou…
We investigate the decoherence properties of a central system composed of two spins 1/2 in contact with a spin bath. The dynamical regime of the bath ranges from a fully integrable integrable limit to complete chaoticity. We show that the dynamical regime of the bath determines the efficiency of the decoherence process. For perturbative regimes, the integrable limit provides stronger decoherence, while in the strong coupling regime the chaotic limit becomes more efficient. We also show that the decoherence time behaves in a similar way. On the contrary, the rate of decay of magnitudes like lin…
The destruction of quantum-mechanical phase coherence by a fluctuating quantum bath has been investigated mostly for a single particle. However, for electronic transport through disordered samples and mesoscopic interference setups, we have to treat a many-fermion system subject to a quantum bath. Here, we review a novel technique for treating this situation in the case of ballistic interferometers, and discuss its application to the electronic Mach-Zehnder setup. We use the results to bring out the main features of decoherence in a many-fermion system, and briefly discuss the same ideas in th…
We consider a quantum model of a nanomechanical flexing beam resonator interacting with a bath comprising a few damped tunneling two level systems (TLS's). In contrast with a resonator interacting bilinearly with an ohmic free oscillator bath (modeling clamping loss, for example), the mechanical resonator damping is amplitude dependent, while the decoherence of quantum superpositions of mechanical position states depends only weakly on their spatial separation.
We study the decay process in an open system, emphasizing on the relevance of the environment's spectral structure. Non-Markovian effects are included to quantitatively analyze the degradation rate of the coherent evolution. The way in which a two level system is coupled to different environments is specifically addressed: multiple connections to a single bath (public environment)or single connections to multiple baths (private environments). We numerically evaluate the decay rate of a local excitation by using the Survival Probability and the Loschmidt Echo. These rates are compared to analyt…
Short time approximation is developed for system-environmental bath mode interactions involving a general non-Hermitian system operator $Λ$, and its conjugate, $Λ^\dagger$, in order to evaluate onset of decoherence at low temperatures in quantum systems interacting with environment. The developed approach is complementary to Markovian approximations and appropriate for evaluation of quantum computing schemes. Example of a spin system coupled to a bosonic heat bath via $Λ\propto σ_-$ is worked out in detail.
This Letter deals with the time evolution of a qubit weakly coupled to a reservoir which has a symmetry broken state with long range order at finite temperatures. In particular, we model the ordered reservoir by a standard BCS superconductor with s-wave pairing. We study the reduced density matrix of a qubit using both the time-convolutionless and Nakajima-Zwanzig approximations. We study different kinds of couplings between the qubit and the superconducting bath. We find that ordering in the superconducting bath generically leads to an unfavorable non- Markovian faster-than-exponential decay …
Decoherence of a localized electron spin in a solid state material (the ``central spin'' problem) at low temperature is believed to be dominated by interactions with nuclear spins in the lattice. This decoherence is partially suppressed through the application of a large magnetic field that splits the energy levels of the electron spin and prevents depolarization. However, dephasing decoherence resulting from a dynamical nuclear spin bath cannot be removed in this way. Fluctuations of the nuclear field lead to uncertainty of the electron's precessional frequency in a process known as spectral …
We investigate in detail, using both analytical and numerical tools, the decoherence of electron spins in quantum dots (QDs) coupled to a bath of nuclear spins in magnetic fields or with various initial bath polarizations, focusing on the longitudinal relaxation in low and moderate field/polarization regimes. An increase of the initial polarization of nuclear spin bath has the same effect on the decoherence process as an increase of the external magnetic field, namely, the decoherence dynamics changes from smooth decay to damped oscillations. This change can be observed experimentally for a si…
We study the dynamics of impurity bound electrons interacting with a bath of conduction band electrons in a semiconductor. Only the exchange interaction is considered. We derive master equations for the density matrices of single and two qubit systems under the usual Born and Markov approximations. The bath mediated RKKY interaction in the two qubit case arises naturally. It leads to an energy shift significant only when the ratio ($R_{T}$) of the inter-qubit distance to the thermal deBroglie wavelength of the bath electrons is small. This bath mediated interaction also has a profound impact o…
We report coherent manipulation of S=10 Fe$_{8}$ single-molecule magnets. The temperature dependence of the spin decoherence time $T_2$ measured by high frequency pulsed electron paramagnetic resonance indicates that strong spin decoherence is dominated by Fe$_{8}$ spin bath fluctuations. By polarizing the spin bath in Fe$_{8}$ single-molecule magnets at magnetic field $B$ = 4.6 T and temperature $T$ = 1.3 K, spin decoherence is significantly suppressed and extends the spin decoherence time $T_2$ to as long as 712 ns. A second decoherence source is likely due to fluctuations of the nuclear spi…
We study the decoherence of a qubit weakly coupled to frustrated spin baths. We focus on spin-baths described by the classical Ising spin glass and the quantum random transverse Ising model which are known to have complex thermodynamic phase diagrams as a function of an external magnetic field and temperature. Using a combination of numerical and analytical methods, we show that for baths initally in thermal equilibrium, the resulting decoherence is highly sensitive to the nature of the coupling to the environment and is qualitatively different in different parts of the phase diagram. We find …
In double quantum dots, the exchange interaction between two electron spins renormalizes the excitation energy of pair-flips in the nuclear spin bath, which in turn modifies the non-Markovian bath dynamics. As the energy renormalization varies with the Overhauser field mismatch between the quantum dots, the electron singlet-triplet decoherence resulting from the bath dynamics depends on sampling of nuclear spin states from an ensemble, leading to the transition from exponential decoherence in single-sample dynamics to power-law decay under ensemble averaging. In contrast, the decoherence of a …
We study theoretically the phonon-induced relaxation and decoherence processes in the hybrid qubit in silicon. Hybrid qubit behaves as a charge qubit when the detuning is close to zero and as spin qubit for large detuning values. It is realized starting from an electrostatically defined double quantum dot where three electrons are confined and manipulated through only electrical tuning. By employing a three-level effective model for the qubit and describing the environment bath as a series of harmonic oscillators in the thermal equilibrium states, we extract the relaxation and decoherence time…
We present a combination of analytic calculations and a powerful numerical method for large spin baths in the low-field limit. The hyperfine interaction between the central spin and the bath is fully captured by the density matrix renormalization group. The adoption of the density matrix renormalization group for the central spin model is presented and a proper method for calculating the real-time evolution at infinite temperature is identified. In addition, we study to which extent a semiclassical model, where a quantum spin-1/2 interacts with a bath of classical Gaussian fluctuations, can ca…
The dynamics and decoherence of an electronic spin-1/2 qubit coupled to a bath of nuclear spins via hyperfine interactions in a quantum dot is studied. We show how exact results from the integrable solution can be used to understand the dynamic behavior of the qubit. It is possible to predict the main frequency contributions and their broadening for relatively general initial states analytically, leading to an estimate of the corresponding decay times. Furthermore, for a small bath polarization, a new low-frequency time scale is observed.
We investigate the decoherence process for a quantum register composed of N qubits coupled to an environment. We consider an environment composed of one common phonon bath and several electronic baths. This environment is relevant to the implementation of a charge based solid-state quantum computer. We explicitly compute the time evolution of all off-diagonal terms of the register's reduced density matrix. We find that in realistic configurations, "superdecoherence" and "decoherence free subspaces" do not exist for an N-qubit system. This means that all off-diagonal terms decay like exp(-q(t)N…
Coherence evolution and echo effect of an electron spin, which is coupled inhomogeneously to an interacting one-dimensional finite spin bath via hyperfine-type interaction, is studied using the adaptive time dependent density matrix renormalization group (t-DMRG) method. It is found that the interplay of the coupling inhomogeneity and the transverse intra-bath interactions results in two qualitatively different coherence evolutions, namely, a coherence preserving evolution characterized by periodic oscillation and a complete decoherence evolution. Correspondingly, the echo effects induced by a…
We investigate decoherence due to pure dephasing of a localized spin qubit interacting with a nuclear spin bath. Although in the limit of a very large magnetic field the only decoherence mechanism is spectral diffusion due to dipolar flip-flops of nuclear spins, with decreasing field the hyperfine-mediated interactions between the nuclear spins become important. We take advantage of their long-range nature, and resum the leading terms in an 1/N expansion of the decoherence time-evolution function (N, being the number of nuclear spins interacting appreciably with the electron spin, is large). F…
We consider quantum decoherence in solid-state systems by studying the transverse dynamics of a single qubit interacting with a fermionic bath and driven by external pulses. Our interest is in investigating the extent to which the lost coherence can be restored by the application of external pulses to the qubit. We show that the qubit evolution under various pulse sequences can be mapped onto Keldysh path integrals. This approach allows a simple diagrammatic treatment of different bath excitation processes contributing to qubit decoherence. We apply this theory to the evolution of the qubit co…
We systematically investigate the universal spin decoherence dynamics of a localized electron in an arbitrary nuclear spin bath, which can be even far away from equilibrium due to the weak nuclear-lattice interaction. We show that the electron spin relaxation dynamics (as well as spin pure dephasing and Hahn echo decay) can {\it always} have a universal behavior as long as the initial state is composed of a sufficiently large amount of spin eigenstates. For a given system, the pattern of the universal dynamics depends on the complicated initial condition only via a {\it single} parameter, whic…
We investigate the quantum Zeno and anti-Zeno effects in spin bath models: the spin-boson model and a spin-fermion model. We show that the Zeno-anti-Zeno transition is critically controlled by the system-bath coupling parameter, the same parameter that determines spin decoherence rate. We also discuss the crossover in a biased system, at high temperatures, and for a nonequilibrium spin-fermion system, manifesting the counteracting roles of electrical bias, temperature, and magnetic field on the spin decoherence rate.
We consider pure dephasing of Bell states of electron spin qubits interacting with a sparse bath of nuclear spins. Using the newly developed two-qubit generalization of cluster correlation expansion method, we calculate the spin echo decay of $|Ψ\rangle$ and $|Φ\rangle$ states for various interqubit distances. Comparing the results with calculations in which dephasing of each qubit is treated independently, we identify signatures of influence of common part of the bath on the two qubits. At large interqubit distances, this common part consists of many nuclei weakly coupled to both qubits, so t…
Braiding Majorana zero-modes around each other is a promising route towards topological quantum computing. Yet, two competing maxims emerge when implementing Majorana braiding in real systems: On the one hand, perfect braiding should be conducted adiabatically slowly to avoid non-topological errors. On the other hand, braiding must be conducted fast such that decoherence effects introduced by the environment are negligible, which are generally unavoidable in finite-size systems. This competition results in an intermediate time scale for Majorana braiding that is optimal, but generally not erro…
We study decoherence of a field-driven qubit in the presence of environmental noises. For a general qubit, we find that driving, whether on-resonance or off-resonance, alters the qubit decoherence rates (including dissipation and pure dephasing), allowing both blue and red sideband contributions from the reservoir. Depending on the noise spectral density, driving field detuning and driving field phase shift, the qubit decoherence rates could be either accelerated or reduced. We apply our general theory to the system of an electron spin qubit that is confined in a quantum dot and driven by an i…
We study the influence of narrowed distributions of the nuclear Overhauser field on the decoherence of a central electron spin in quantum dots. We describe the spin dynamics in quantum dots by the central spin model. We use analytic solutions for uniform couplings and the time dependent density-matrix renormalization group (tDMRG) for nonuniform couplings. With these tools we calculate the dynamics of the central spin for large baths of nuclear spins with or without external magnetic field applied to the central spin. The focus of our study is the influence of initial mixtures with narrowed di…
We present an approach that allows quantifying decoherence processes in an open quantum system subject to external time-dependent control. Interactions with the environment are modeled by a standard bosonic heat bath. We develop two unitarity-preserving approximation schemes to calculate the reduced density matrix. One of the approximations relies on a short-time factorization of the evolution operator, while the other utilizes expansion in terms of the system-bath coupling strength. Applications are reported for two illustrative systems: an exactly solvable adiabatic model, and a model of a r…
