Dynamics of collective decoherence and thermalization

We analyze the dynamics of N interacting spins (quantum register) collectively coupled to a thermal environment. Each spin experiences the same environment interaction, consisting of an energy conserving and an energy exchange part.We find the decay rates of the reduced density matrix elements in the energy basis. We show that if the spins do not interact among each other, then the fastest decay rates of off-diagonal matrix elements induced by the energy conserving interaction is of order N², while that one induced by the energy exchange interaction is of the order N only. Moreover, the diagonal matrix elements approach their limiting values at a rate independent of N. For a general spin system the decay rates depend in a rather complicated (but explicit) way on the size N and the interaction between the spins.Our method is based on a dynamical quantum resonance theory valid for small, fixed values of the couplings. We do not make Markov-, Born- or weak coupling (van Hove) approximations.     

Quantum coherence and correlation dynamics of two-qubit system in spin bath environment

The quantum entanglement,discord,and coherence dynamics of two spins in the model of a spin coupled to a spin bath through an intermediate spin are studied.The effects of the important physical parameters including the coupling strength of two spins,the interaction strength between the intermediate spin and the spin bath,the number of bath spins and the temperature of the system on quantum coherence and correlation dynamics are discussed in different cases.The frozen quantum discord can be observed whereas coherence does not when the initial state is the Bell-diagonal state.At finite temperature,we find that coherence is more robust than quantum discord,which is better than entanglement,in terms of resisting the influence of environment.Therefore,quantum coherence is more tenacious than quantum correlation as an important resource.     

Finite-temperature scaling of quantum coherence near criticality in a spin chain

We explore quantum coherence, inherited from Wigner-Yanase skew information, to analyzequantum criticality in the anisotropic XY chain model at finite temperature. Based on theexact solutions of the Hamiltonian, the quantum coherence contained in a nearest-neighborspin pairs reduced density matrix ρ is obtained. The first-order derivative of thequantum coherence is non-analytic around the critical point at sufficient low temperature.The finite-temperature scaling behavior and the universality are verified numerically. Inparticular, the quantum coherence can also detect the factorization transition in such amodel at sufficient low temperature. We also show that quantum coherence contained indistant spin pairs can characterize quantum criticality and factorization phenomena atfinite temperature. Our results imply that quantum coherence can serve as an efficientindicator of quantum criticality in such a model and shed considerable light on therelationships between quantum phase transitions and quantum information theory at finitetemperature.     

Quantum computation using the 13C nuclear spins near the single NV defect center in diamond

We discuss the possibility of realizing quantum computation on the basis of a cluster of single interacting nuclear spins in solids. This idea seems to be feasible because of the combination of two techniques—Single Molecule Spectroscopy and Optically Detected Electron Nuclear Double Resonance. Compared to the well-known bulk Nuclear Magnetic Resonance (NMR), the proposed method of quantum computation has the advantage that quantum computation is performed with pure spin states and the quantum processor is more easily scalable. At the same time, the advantages of NMR quantum computation are kept: long coherence time and easy construction of quantum gates. As a specific system to implement the above idea, we discuss the ¹³C-nuclear spins in the nearest vicinity of a single nitrogen-vacancy (NV) defect center in diamond, which can be optically detected using the technique of scanning confocal microscopy. Owing to the hyperfine coupling of the ground state electron paramagnetic spin S=1 of the center to ¹³C nuclear spins in a diamond lattice, the states of nuclear spins in the vicinity of the defect-center can be addressed individually. Preliminary consideration shows that it should be possible to address up to 12 individual ¹³C nuclear spins. The dephasing time of the nuclear spin states at low temperatures allows realization up to 10⁵ gates.     

Spin state selective coherence transfer: a method for discrimination and complete analyses of the overlapped and unresolved 1H NMR spectra of enantiomers

In general, the proton NMR spectra of chiral molecules aligned in the chiral liquid crystalline media are broad and featureless. The analyses of such intricate NMR spectra and their routine use for spectral discrimination of R and S optical enantiomers are hindered. A method is developed in the present study which involves spin state selective two dimensional correlation of higher quantum coherence to its single quantum coherence of a chemically isolated group of coupled protons. This enables the spin state selective detection of proton single quantum transitions based on the spin states of the passive nuclei. The technique provides the relative signs and magnitudes of the couplings by overcoming the problems of enantiomer discrimination, spectral complexity and poor resolution, permitting the complete analyses of the otherwise broad and featureless spectra. A non-selective 180 degrees pulse in the middle of MQ dimension retains all the remote passive couplings. This accompanied by spin selective MQ-SQ conversion leads to spin state selective coherence transfer. The removal of field inhomogeneity contributes to dramatically enhanced resolution. The difference in the cumulative additive values of chemical shift anisotropies and the passive couplings, between the enantiomers, achieved by detecting Nth quantum coherence of N magnetically equivalent spins provides enhanced separation of enantiomer peaks. The developed methodology has been demonstrated on four different chiral molecules with varied number of interacting spins, each having a chiral centre.     

Restoring coherence lost to a slow interacting mesoscopic spin bath

For a two-state quantum object interacting with a slow mesoscopic interacting spin bath, we show that a many-body solution of the bath dynamics conditioned on the quantum-object state leads to an efficient control scheme to recover the lost quantum-object coherence through disentanglement. We demonstrate the theory with the realistic problem of one electron spin in a bath of many interacting nuclear spins in a semiconductor quantum dot. The spin language can be easily generalized to a quantum object in contact with a bath of interacting multilevel quantum units with the caveat that the bath is mesoscopic and its dynamics is slow compared with the quantum object.     

Multiple Quantum Coherences (MQ) NMR and Entanglement Dynamics in the Mixed-Three-Spin XXX Heisenberg Model with Single-Ion Anisotropy

We analytically investigate Multiple Quantum (MQ) NMR dynamics in a mixed-three-spin (1/2,1,1/2) system with XXX Heisenberg model at the front of an external homogeneous magnetic field B. A single-ion anisotropy property ζ is considered for the spin-1. The intensities dependence of MQ NMR coherences on their orders (zeroth and second orders) for two pairs of spins (1,1/2) and (1/2,1/2) of the favorite tripartite system are obtained. It is also investigated dynamics of the pairwise quantum entanglement for the bipartite (sub)systems (1,1/2) and (1/2,1/2) permanently coupled by, respectively, coupling constants J₁ and J₂, by means of concurrence and fidelity. Then, some straightforward comparisons are done between these quantities and the intensities of MQ NMR coherences and ultimately some interesting results are reported. We also show that the time evolution of MQ coherences based on the reduced density matrix of the pair spins (1,1/2) is closely connected with the dynamics of the pairwise entanglement. Finally, we prove that one can introduce MQ coherence of the zeroth order corresponds to the pair spins (1,1/2) as an entanglement witness at some special time intervals.     

Direct observation of quantum coherence in single-molecule magnets

Direct evidence of quantum coherence in a single-molecule magnet in a frozen solution is reported with coherence times as long as T{2}=630+/-30 ns. We can strongly increase the coherence time by modifying the matrix in which the single-molecule magnets are embedded. The electron spins are coupled to the proton nuclear spins of both the molecule itself and, interestingly, also to those of the solvent. The clear observation of Rabi oscillations indicates that we can manipulate the spin coherently, an essential prerequisite for performing quantum computations.     

Isotopically engineered Si and Ge for spintronics and quantum computation

Si, Ge as well as SiGe structures are the promising materials for spintronics and quantum computation due to the fact that in both crystals only one isotope (²⁹Si and ⁷³Ge) has nuclear spin. As a result, isotope engineering of Si and Ge permits to control the density of nuclear spins and vary the spin coherence time, a crucial parameter in spintronics. In the first part we discuss the NMR study of nuclear spin decoherence in Ge single crystals with different abundance of the ⁷³Ge isotope. It was observed that the slow component of the dephasing process is elongated with depletion of Ge crystal with isotope ⁷³Ge. The second part is devoted to the development of the Kane's model of nuclear spin-based quantum computer, which uses the nuclear spin of ³¹P impurity atoms in a ²⁸Si matrix as quantum bits (qubits). We discuss a new method of placing ³¹P atoms in a ²⁸Si based on neutron-transmutation-doping of isotopically engineered Si and Ge. In the proposed structure, interqubit coupling is due to indirect hyperfine interaction of ³¹P nuclear spins with electrons localized in a ²⁸Si quasi-one-dimensional nanowire, which allows one to control the coupling between distant qubits.     

Optical nuclear spin polarization in quantum dots

Hyperfine interaction between electron spin and randomly oriented nuclear spins is a key issue of electron coherence for quantum information/computation. We propose an efficient way to establish high polarization of nuclear spins and reduce the intrinsic nuclear spin fluctuations. Here, we polarize the nuclear spins in semiconductor quantum dot(QD) by the coherent population trapping(CPT) and the electric dipole spin resonance(EDSR) induced by optical fields and ac electric fields. By tuning the optical fields, we can obtain a powerful cooling background based on CPT for nuclear spin polarization. The EDSR can enhance the spin flip–flop rate which may increase the cooling efficiency. With the help of CPT and EDSR, an enhancement of 1300 times of the electron coherence time can be obtained after a 10-ns preparation time.     

Entanglement and elementary excitations in quantum spin chain

The entanglement induced by elementary excitations in the XX spin chain is investigated by Bethe ansatz method. The reduced density matrix and correlation function between any pair of spins can be obtained for ground and all excited states with N qubits. Rely on them we show the explicit and general relations between entanglement and elementary excitations in XX spin chain. We further show our method can be extend to other integrable models.     

Diagonal entropy in many-body systems: Volume effect and quantum phase transitions

We investigate the diagonal entropy(DE) of the ground state for quantum many-body systems, including the XY model and the Ising model with next nearest neighbor interactions. We focus on the DE of a subsystem of L continuous spins. We show that the DE in many-body systems, regardless of integrability, can be represented as a volume term plus a logarithmic correction and a constant offset. Quantum phase transition points can be explicitly identified by the three coefficients thereof. Besides, by combining entanglement entropy and the relative entropy of quantum coherence, as two celebrated representatives of quantumness, we simply obtain the DE, which naturally has the potential to reveal the information of quantumness. More importantly, the DE is concerning only the diagonal form of the ground state reduced density matrix, making it feasible to measure in real experiments, and therefore it has immediate applications in demonstrating quantum supremacy on state-of-the-art quantum simulators.     

Numerical modeling of the central spin problem using the spin-coherent-state representation

In this work, we consider decoherence of a central spin by a spin bath. In order to study the nonperturbative decoherence regimes, we develop an efficient mean-field-based method for modeling the spin-bath decoherence, based on the representation of the central spin density matrix. The method can be applied to longitudinal and transverse relaxation at different external fields. In particular, by modeling large-size quantum systems (up to 16 000 bath spins), we make controlled predictions for the slow long-time decoherence of the central spin.     

Persistent narrowing of nuclear-spin fluctuations in InAs quantum dots using laser excitation

We demonstrate the suppression of nuclear-spin fluctuations in an InAs quantum dot and measure the timescales of the spin narrowing effect. By initializing for tens of milliseconds with two continuous wave diode lasers, fluctuations of the nuclear spins are suppressed via the hole-assisted dynamic nuclear polarization feedback mechanism. The fluctuation narrowed state persists in the dark (absent light illumination) for well over 1 s even in the presence of a varying electron charge and spin polarization. Enhancement of the electron spin coherence time (T2*) is directly measured using coherent dark state spectroscopy. By separating the calming of the nuclear spins in time from the spin qubit operations, this method is much simpler than the spin echo coherence recovery or dynamic decoupling schemes.     

Exact solutions in the dynamics of alternating open chains of spins s = 1/2 with the XY Hamiltonian and their application to problems of multiple-quantum dynamics and quantum information theory

A method for exactly diagonalizing the XY Hamiltonian of an alternating open chain of spins s = 1/2 has been proposed on the basis of the Jordan-Wigner transformation and analysis of the dynamics of spinless fermions. The multiple-quantum spin dynamics of alternating open chains at high temperatures has been analyzed and the intensities of multiple-quantum coherences have been calculated. The problem of the transfer of a quantum state from one end of the alternating chain to the other is studied. It has been shown that the ideal transfer of qubits is possible in alternating chains with a larger number of spins than that in homogeneous chains.     

Exact calculation,using angular momentum,of combined Zeeman and quadrupolar interactions in NMR

The NMR of nuclei with spins greater than ½ is often strongly influenced by the quadrupole interaction. This combination of Zeeman and quadrupole terms can usually be treated using perturbation theory, but an exact calculation is also needed. We explain an exact approach that eliminates the evaluation of commutators of complicated operators. Instead, the calculation is based on matrix elements of the Liouvillian, the commutator with the Hamiltonian. The spectrum can then be calculated directly from the eigenvectors and eigenvalues of the Liouvillian. With the aid of angular momentum methods, it can be shown that the quadupole interaction for spin I is fully determined by only (2I ?1) reduced matrix elements—for spin 3/2, this means only two quantities. The exact nature of the various basis operators is not needed, since the calculation only needs the angular momentum quantum numbers. The full Liouvillian matrix can be calculated from selection rules and the Wigner-Eckart theorem. Furthermore, we present an expression for these reduced matrix elements which is valid for any spin. This theory covers the whole range from quadrupole-perturbed NMR spectra to Zeeman-perturbed nuclear quadrupole resonance.     

Non-equilibrium thermal entanglement for a three spin chain

The dynamics of a chain of three spins coupled at both ends to separate bosonic baths at different temperatures is studied. An exact analytical solution of the master equation in the Born-Markov approximation for the reduced density matrix of the chain is constructed. It is shown that for long times the reduced density matrix converges to the non-equilibrium steady state. Dynamical and steady state properties of the concurrence between the first and the last spin are studied.     

基于金刚石氮-空位色心自旋系综与超导量子电路混合系统的量子节点纠缠

量子纠缠是实现量子计算和量子通信的核心基础,本文提出了在金刚石氮-空位色心(NV centers)自旋系综与超导量子电路耦合的混合系统中实现两个分离量子节点之间纠缠的理论方案.在该混合系统中,把金刚石NV centers自旋系综和与之耦合的超导共面谐振器视为一个量子节点,两个量子节点之间通过一个空的超导共面谐振器连接.具有较长相干时间的NV centers自旋系综作为一个量子存储器,用于制备、存储和发送量子信息;易于外部操控的超导量子电路可执行量子逻辑门操作,快速调控量子信息.为了实现两个分离量子节点之间的纠缠,首先对系统的哈密顿量进行正则变换,将其等价为两个NV centers自旋系综与同一个超导共面谐振器之间的JC耦合;然后采用NV centers自旋-光子混合比特编码的方式,通过调节超导共面谐振器的谐振频率,精确控制体系演化时间,高保真度地实现了两个分离量子节点之间的量子纠缠.本方案还可以进一步扩展和集成,用于构建多节点纠缠的分布式量子网络.     

Low temperature MQ NMR dynamics in dipolar ordered state

We investigate analytically and numerically the Multiple Quantum (MQ) NMR dynamics in dipolar ordered spin systems of nuclear spins 1/2 at low temperatures. We consider two different methods of MQ NMR. One of them is based on the measurement of the dipolar energy. The other method uses an additional resonance (π/4)_y-pulse after the preparation period of the standard MQ NMR experiment in solids and allows one to measure the Zeeman energy. Both considered methods are sensitive to the contribution of remote spins in the interaction and to the spin system structure. The QS method is sensitive to the spin number in the molecule while the PS method gives very similar time dependencies of the intensities of MQ coherences for different spin numbers. It is shown that the use of the dipolar ordered initial state has the advantage of exciting the highest order MQ coherences in clusters of 4m identical spins, where m=1,2,3,…, that is impossible to do with the standard MQ method. MQ NMR methods based on the dipolar ordered initial states at low temperatures complement the standard NMR spectroscopy for better studying structures and dynamic processes in solids.