We study decoherence induced on a two-level system coupled to a one-dimensional quantum spin chain. We consider the cases where the dynamics of the chain is determined by the Ising, XY, or Heisenberg exchange Hamiltonian. This model of quantum baths can be of fundamental importance for the understanding of decoherence in open quantum systems, since it can be experimentally engineered by using atoms in optical lattices. As an example, here we show how to implement a pure dephasing model for a qubit system coupled to an interacting spin bath. We provide results that go beyond the case of a central spin coupled uniformly to all the spins of the bath, in particular showing what happens when the bath enters different phases, or becomes critical; we also study the dependence of the coherence loss on the number of bath spins to which the system is coupled and we describe a coupling-independent regime in which decoherence exhibits universal features, irrespective of the system-environment coupling strength. Finally, we establish a relation between decoherence and entanglement inside the bath. For the Ising and the XY models we are able to give an exact expression for the decay of coherences, while for the Heisenberg bath we resort to the numerical time-dependent Density Matrix Renormalization Group.
We study the decoherence of two coupled spins that interact with a chaotic spin-bath environment. It is shown that connectivity of spins in the bath is of crucial importance for the decoherence of the central system. The previously found phenomenon of two-step decoherence (Phys. Rev. Lett. {\bf 90}, 210401 (2003)) turns out to be typical for the bath with a slow enough dynamics or no dynamics. For a generic random system with chaotic dynamics a conventional exponential relaxation to the pointer states takes place. Our results confirm a conjecture of Paz and Zurek (Phys. Rev. Lett. {\bf 82}, 51…
We introduce, and determine decoherence for, a wide class of non-trivial quantum spin baths which embrace Ising, XY and Heisenberg universality classes coupled to a two-level system. For the XY and Ising universality classes we provide an exact expression for the decay of the loss of coherence beyond the case of a central spin coupled uniformly to all the spins of the baths which has been discussed so far in the literature. In the case of the Heisenberg spin bath we study the decoherence by means of the time-dependent density matrix renormalization group. We show how these baths can be enginee…
We study the decoherence of two coupled spins that interact with a spin-bath environment. It is shown that the connectivity and the coupling strength between the spins in the environment are of crucial importance for the decoherence of the central system. For the anisotropic spin-bath, changing the connectivity or coupling strenghts changes the decoherence of the central system from Gaussian to exponential decay law. The initial state of the environment is shown to affect the decoherence process in a qualitatively significant manner.
The well-known increase of the decoherence rate with the temperature, for a quantum system coupled to a linear thermal bath, holds no longer for a different bath dynamics. This is shown by means of a simple classical non-linear bath, as well as a quantum spin-boson model. The anomalous effect is due to the temperature dependence of the bath spectral profile. The decoherence reduction via the temperature increase can be relevant for the design of quantum computers.
We numerically investigate decoherence of a two-spin system (central system) by a bath of many spins 1/2. By carefully adjusting parameters, the dynamical regime of the bath has been varied from quantum chaos to regular, while all other dynamical characteristics have been kept practically intact. We explicitly demonstrate that for a many-body quantum bath, the onset of quantum chaos leads to significantly faster and stronger decoherence compared to an equivalent non-chaotic bath. Moreover, the non-diagonal elements of the system's density matrix decay differently for chaotic and non-chaotic ba…
Using the numerical path integral method we investigate the decoherence and relaxation of qubits in spin-boson (SB) and spin-intermediate harmonic oscillator (IHO)-bath (SIB) models. The cases that the environment baths with low and medium frequencies are investigated. It is shown that the qubits in SB and SIB models have the same decoherence and relaxation as the baths with low frequencies. However, the qubits in the two models have different decoherence and relaxation as the baths with medium frequencies. The decoherence and relaxation of the qubit in SIB model can be modulated through chang…
The works on decoherence due to spin baths usually agree in studying a one-spin system in interaction with a large spin bath. In this paper we generalize those models by analyzing a many-spin system and by studying decoherence or its suppression in function of the relation between the numbers of spins of the system and the bath. This model may help to identify clusters of particles unaffected by decoherence, which, as a consequence, can be used to store quantum information.
We demonstrate in a very general fashion, considerable slowing down of decoherence and relaxation by fast frequency modulation of the system heat bath coupling. The slowing occurs as the decoherence rates are now determined by the spectral components of bath correlations which are shifted due to fast modulation. We present several examples including the slowing down of the heating of a trapped ion, where the system - bath interaction is not necessarily Markovian.
A low temperature model system consisting of a central spin coupled to a spin-bath is studied to determine whether interaction among bath spins has an effect on central spin dynamics. In the absence of intra-environmental coupling, decoherence of the central spin is fast and irreversible. Strong intra-environmental interaction results in an effective decoupling of the central spin from the bath and suppression of decoherence. Weaker intra-environmental coupling reduces but does not eliminate decoherence. We believe that similar behaviour will be observed in any system with a self-interacting e…
We study the decoherence of two coupled spins that interact with a spin-bath environment. It is shown that the connectivity and the coupling strength between the spins in the environment are of crucial importance for the decoherence of the central system. Changing the connectivity or coupling strenghts changes the decoherence of the central system from Gaussian to exponential decay law.
Using the numerical path integral method we investigate the decoherence and relaxation of qubits coupled to an Ohmic bath directly and via an intermediate harmonic oscillator (IHO). Here, we suppose the oscillation frequencies of the bath modes are higher than the IHO's. When we choose suitable parameters the qubits in the two models may have almost same decoherence and relaxation times. However, the decoherence and relaxation times of the qubit in the qubit-IHO-bath model can be modulated through changing the coupling coefficients of the qubit-IHO and IHO-bath and the oscillation frequency of…
We study the relation between the sudden death and revival of the entanglement of two qubits in a common squeezed reservoir, and the normal decoherence, by getting closer to the Decoherence Free Subspace and calculating the effect on the death and revival times.
We report an anomalous decoherence phenomenon of a quantum dissipative system in the framework of a stochastic decoupling scheme along with a hierarchical equations-of-motion formalism without the usual Born-Markov or weak coupling approximations. It is found that the decoherence of a two-qubit spin-boson model can be reduced by increasing the bath temperature in strong-coupling regimes. For the weak-coupling situation, we find that the bath temperature may enhance the decoherence. This result is contrary to the common recognition that a higher bath temperature always induces a more severe dec…
We show that the influence of the shared phonon bath considered in H. Hossein-Nejad and G. D. Scholes, New J. Phys. 12, 065045 (2010) on the exciton transfer in a two-molecule system can be reproduced by that of an independent bath model.
In this paper we propose a closed-system perspective to study decoherence. From this perspective we analyze the spin-bath model as presented in the literature, and a natural generalization of that model. On the basis of the results obtained from that analysis, we argue that decoherence may be understood as a phenomenon relative to the partition of a closed system, selected in each particular case. This viewpoint frees the decoherence program from certain conceptual difficulties derived from its open-system perspective. We also argue that the usual picture of decoherence in terms of energy diss…
We examine the influence of environmental interactions on simple quantum systems by obtaining the exact reduced dynamics of a qubit coupled to a one-dimensional spin bath. In contrast to previous studies, both the qubit-bath coupling and the nearest neighbor intrabath couplings are taken as the spin-flip XX-type. We first study the Rabi oscillations of a single qubit with the spin bath prepared in a spin coherent state, finding that nonresonance and finite intrabath interactions have significant effects on the qubit dynamics. Next, we discuss the bath-induced decoherence of the qubit when the …
The monogamous nature of entanglement has been illustrated by the derivation of entanglement sharing inequalities - bounds on the amount of entanglement that can be shared amongst the various parts of a multipartite system. Motivated by recent studies of decoherence, we demonstrate an interesting manifestation of this phenomena that arises in system-environment models where there exists interactions between the modes or subsystems of the environment. We investigate this phenomena in the spin-bath environment, constructing an entanglement sharing inequality bounding the entanglement between a c…
I present the exact solution of a toy model for gravitationally induced decoherence. The toy model has Hamiltonian resembling optomechanical systems. It is an oscillator system coupled through its energy to an oscillator heat bath. I find the decoherence effect of vacuum fluctuations at zero temperature. Also for a finite bath I show that the decoherence is in general present and the system does not return to its initial coherence unless the fundamental frequencies of the bath have rational ratios.
We study the quantum dynamics of a single qubit coupled to a bath of interacting spins as a model for decoherence in solid state quantum memories. The spin bath is described by the Lipkin-Meshkov-Glick model and the bath spins are subjected to a transverse magnetic field. We investigate the qubit interacting via either an Ising- or an XY-type coupling term to subsets of bath spins of differing size. The large degree of symmetry of the bath allows us to find parameter regimes where the initial qubit state is revived at well defined times after the qubit preparation. These times may become indep…
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…
The effect of chaotic bath dynamics on the decoherence of a quantum system is examined for the vibrational degrees of freedom of a diatomic molecule in a realistic, constant temperature collisional bath. As an example, the specific case of I$_2$ in liquid xenon is examined as a function of temperature, and the results compared with an integrable xenon bath. A crossover in behavior is found: the integrable bath induces more decoherence at low bath temperatures than does the chaotic bath, whereas the opposite is the case at the higher bath temperatures. These results, verifying a conjecture due …
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…
The dynamics of two coupled spins-1/2 coupled to a spin-bath is studied as an extended model of the Tessieri-Wilkie Hamiltonian \cite{TWmodel}. The pair of spins served as an open subsystem were prepared in one of the Bell states and the bath consisted of some spins-1/2 is in a thermal equilibrium state from the very beginning. It is found that with the increasing the coupling strength of the bath spins, the bath forms a resonant antiferromagnetic order. The polarization correlation between the two spins of the subsystem and the concurrence are recovered in some extent to the isolated subsyste…
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…
The longitudinal coupling of a system to the bath usually induces the pure dephasing of the system. In this paper, we study the collective dephasing induced dissipation and decoherence in a coupled-qubit system with a common bath. It is shown that, compared with the case of the same system with independent baths, the interference between the dephasing processes of different qubits induced by the common bath significantly changes the dissipation of the system. For the system of two coupled qubits, the interference leads to a faster decoherence in the non-single-excitation subspaces and a slower…
In this paper we study the decoherence and purity of a driven solid-state qubit in the Ohmic bath by using the method based on the master equation. At first, instead of solving the master equation we investigate the coefficients of the equation which describe the shift in frequency, diffusive, decoherence, and so on. It is shown that one of the coefficients (we called it decoherence coefficient) is crucial to the decoherence of the qubit in the model. Then we investigate the evolution of the purity of the state in the model. From the analysis of the purity we see that the decoherence time of t…
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…
We demonstrate that the Chebyshev expansion method is a very efficient numerical tool for studying spin-bath decoherence of quantum systems. We consider two typical problems arising in studying decoherence of quantum systems consisting of few coupled spins: (i) determining the pointer states of the system, and (ii) determining the temporal decay of quantum oscillations. As our results demonstrate, for determining the pointer states, the Chebyshev-based scheme is at least a factor of 8 faster than existing algorithms based on the Suzuki-Trotter decomposition. For the problems of second type, th…
We consider a free charged particle interacting with an electromagnetic bath at zero temperature. The dipole approximation is used to treat the bath wavelengths larger than the width of the particle wave packet. The effect of these wavelengths is described then by a linear Hamiltonian whose form is analogous to phenomenological Hamiltonians previously adopted to describe the free particle-bath interaction. We study how the time dependence of decoherence evolution is related with initial particle-bath correlations. We show that decoherence is related to the time dependent dressing of the partic…
In this work we find explicitly the decoherence free subspace (DFS) for a two two-level system in a common squeezed vacuum bath. We also find an orthogonal basis for the DFS composed of a symmetrical and an antisymmetrical (under particle permutation) entangled state. For any initial symmetrical state, the master equation has one stationary state which is the symmetrical entangled decoherence free state. In this way, one can generate entanglement via common squeezed bath of the two systems. If the initial state does not have a definite parity, the stationary state depends strongly on the initi…
We study, in the paradigm of open quantum systems, the dynamics of quantum coherence of a static polarizable two-level atom which is coupled with a thermal bath of fluctuating electromagnetic field in the absence and presence of boundaries. The purpose is to find the conditions under which the decoherence can be inhibited effectively. We find that without boundaries, quantum coherence of the two-level atom inevitably decreases due to the effect of thermal bath. However, the quantum decoherence, in the presence of a boundary, could be effectively inhibited when the atom is transversely polariza…
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…
The dynamics of a qubit in two different environments are investigated theoretically. The first environment is a two level system coupled to a bosonic bath. And the second one is a damped harmonic oscillator. Based on a unitary transformation, we find that the decoherence of the qubit can be reduced with increasing temperature $T$ in the first case, which agree with the results in [Phys. Rev. Lett. 100, 120401], whereas, it can not be reduced with $T$ in the second case. In both cases, the qubit dynamics are changed substantially as the coupling increases or finite detuning appears.
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…
Maintaining coherence of a qubit is of vital importance for realizing a large-scale quantum computer in practice. In this work, we study the central spin decoherence problem in the $XXX$ central spin model (CSM) and focus on the quantum states with different initial entanglement, namely intra-bath entanglement or system-bath entanglement. We analytically obtain their evolutions of fidelity, entanglement, and quantum coherence. When the initial bath spins constitute an $N$-particle entangled state (the Greenberger-Horne-Zeilinger-bath or the $W$-bath), the leading amplitudes of their fidelity e…
Coherence in an open quantum system is degraded through its interaction with a bath. This decoherence can be avoided by restricting the dynamics of the system to special decoherence-free subspaces. These subspaces are usually constructed under the assumption of spatially symmetric system-bath coupling. Here we show that decoherence-free subspaces may appear without spatial symmetry. Instead, we consider a model of system-bath interactions in which to first order only multiple-qubit coupling to the bath is present, with single-qubit system-bath coupling absent. We derive necessary and sufficien…
The time evolution of a spin-1/2 particle under the influence of a locally applied external magnetic field, and interacting with anisotropic spin environment in thermal equilibrium at temperature $T$ is studied. The exact analytical form of the reduced density matrix of the central spin is calculated explicitly for finite number of bath spins. The case of an infinite number of environmental spins is investigated using the convergence of the rescaled bath operators to normal Gaussian random variables. In this limit, we derive the analytical form of the components of the Bloch vector for antifer…
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…
A general theory is presented for the treatment of decoherence of a multilevel quantum system (with many degrees of freedom) interacting with multi-bath reservoir and driven by ac fields. In this approach, the system is described by a reduced density operator and the multi-bath reservoir is characterized by a number of spectral densities. The reduced density operator is governed by the master equation in which the effect of ac driving fields and the leakage to non-computational states are included. The theory is applied to the study of decoherence of a two-dimensional (2D) SQUID flux qubit cou…
We investigate the effect of common bath decoherence on the qubits of Alice in the usual teleportation protocol. The system bath interaction is studied under the central spin model, where the qubits are coupled to the bath spins through isotropic Heisenberg interaction. We have given a more generalized representation of the protocol in terms of density matrices and calculated the average fidelity of the teleported state for different Bell state measurements performed by Alice. The common bath interaction differentiates the outcome of various Bell state measurements made by Alice. There will be…
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…
The reduced dynamics of a single or two qubits coupled to an interacting quantum spin bath modeled by a XXZ spin chain is investigated. By using the method of time-dependent density matrix renormalization group (t-DMRG), we go beyond the uniform coupling central spin model and evaluate nonperturbatively the induced decoherence and entanglement. It is shown that both decoherence and entanglement strongly depend on the phase of the underlying spin bath. We show that in general, spin baths can induce entanglement for an initially disentangled pair of qubits. Furthermore, when the spin bath is in …
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…
The "self-induced decoherence" (SID) approach suggests that (1) the expectation value of any observable becomes diagonal in the eigenstates of the total Hamiltonian for systems endowed with a continuous energy spectrum, and (2), that this process can be interpreted as decoherence. We evaluate the first claim in the context of a simple spin bath model. We find that even for large environments, corresponding to an approximately continuous energy spectrum, diagonalization of the expectation value of random observables does in general not occur. We explain this result and conjecture that SID is li…
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…
We study the non-Markovian entanglement dynamics of two qubits in a common squeezed bath. We see remarkable difference between the non-Markovian entanglement dynamics with its Markovian counterpart. We show that a non-Markovian decoherence free state is also decoherence free in the Markovian regime, but all the Markovian decoherence free states are not necessarily decoherence free in the non-Markovian domain. We extend our calculation from squeezed vacuum bath to squeezed thermal bath, where we see the effect of finite bath temperatures on the entanglement dynamics.
We present a method to encode a \textit{dressed} qubit into the product state of an electron spin localized in quantum dot and its surrounding nuclear spins via a dressing transformation. In this scheme, the hyperfine coupling and a portion of nuclear dipole dipole interaction become logic gates, while they are the sources of decoherence in electron spin qubit proposals. We discuss errors and corrections for the dressed qubits. Interestingly, the effective Hamiltonian of nuclear spins is equivalent to a pairing Hamiltonian, which provides the microscopic mechanism to protect dressed qubits aga…
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…
We have studied the effect of a non-Hermitian Bosonic bath on the dynamics of a two-level spin system. The non-Hermitian Hamiltonian of the bath is chosen such that it converges to the harmonic oscillator Hamiltonian when the non-Hermiticity is switched off. We calculate the dynamics of the spin system and found that the non-Hermiticity can have positive as well as negative effects on the coherence of the system. However, the decoherence can be completely eliminated by choosing the non-Hermiticity parameter and the phase of the system bath interaction appropriately. We have also studied the ef…
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…
