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Magnetite (Fe3O4) is of fundamental importance as the original magnetic material and also for the Verwey transition near T_V = 125 K, below which a complex lattice distortion and electron orders occur. The Verwey transition is suppressed by strain or chemical doping effects giving rise to well-documented first and second-order regimes, but the origin of the order change is unclear. Here, we show that slow oxidation of monodisperse Fe3O4 nanoparticles leads to an intriguing variation of the Verwey transition that elucidates the doping effects. Exposure to various fixed oxygen pressures at ambient temperature leads to an initial drop to TV minima as low as 70 K after 45-75 days, followed by recovery to a constant value of 95 K after 160 days that persists in all experiments for aging times up to 1070 days. A physical model based on both doping and doping-gradient effects accounts quantitatively for this evolution and demonstrates that the persistent 95 K value corresponds to the lower limit for homogenously doped magnetite and hence for the first order regime. In comparison, further suppression down to 70 K results from inhomogeneous strains that characterize the second-order region. This work demonstrates that slow reactions of nanoparticles can give exquisite control and separation of homogenous and inhomogeneous doping or strain effects on an nm scale and offers opportunities for similar insights into complex electronic and magnetic phase transitions in other materials., Comment: 24 pages, 13 figures, 2 tables, the manuscript is accepted for publishing at Nature Communications

Modulation of donor electron wavefunction via electric fields is vital to quantum computing architectures based on donor spins in silicon. For practical and scalable applications, the donor-based qubits must retain sufficiently long coherence times in any realistic experimental conditions. Here, we present pulsed electron spin resonance studies on the longitudinal $(T_1)$ and transverse $(T_2)$ relaxation times of phosphorus donors in bulk silicon with various electric field strengths up to near avalanche breakdown in high magnetic fields of about 1.2 T and low temperatures of about 8 K. We find that the $T_1$ relaxation time is significantly reduced under large electric fields due to electric current, and $T_2$ is affected as the $T_1$ process can dominate decoherence. Furthermore, we show that the magnetoresistance effect in silicon can be exploited as a means to combat the reduction in the coherence times. While qubit coherence times must be much longer than quantum gate times, electrically accelerated $T_1$ can be found useful when qubit state initialization relies on thermal equilibration., Comment: 7 pages, 5 figures

Most interesting phenomena of condensed matter physics originate from interactions among different degrees of freedom, making it a very intriguing yet challenging question how certain ground states emerge from only a limited number of atoms in assembly. This is especially the case for strongly correlated electron systems with overwhelming complexity. The Verwey transition of Fe3O4 is a classic example of this category, of which the origin is still elusive 80 years after the first report. Here we report, for the first time, that the Verwey transition of Fe3O4 nanoparticles exhibits size-dependent thermal hysteresis in magnetization, 57Fe NMR, and XRD measurements. The hysteresis width passes a maximum of 11 K when the size is 120 nm while dropping to only 1 K for the bulk sample. This behavior is very similar to that of magnetic coercivity and the critical sizes of the hysteresis and the magnetic single domain are identical. We interpret it as a manifestation of charge ordering and spin ordering correlation in a single domain. This work paves a new way of undertaking researches in the vibrant field of strongly correlated electron physics combined with nanoscience., Comment: 13 pages, 4 figures

Demonstrating quantum advantage with less powerful but more realistic devices is of great importance in modern quantum information science. Recently, a significant quantum speedup was achieved in the problem of learning a hidden parity function with noise. However, if all data qubits at the query output are completely depolarized, the algorithm fails. In this work, we present a quantum parity learning algorithm that exhibits quantum advantage as long as one qubit is provided with nonzero polarization in each query. In this scenario, the quantum parity learning naturally becomes deterministic quantum computation with one qubit. Then the hidden parity function can be revealed by performing a set of operations that can be interpreted as measuring nonlocal observables on the auxiliary result qubit having nonzero polarization and each data qubit. We also discuss the source of the quantum advantage in our algorithm from the resource-theoretic point of view., Comment: 7 pages, 5 figures. Comments welcome

We demonstrate an efficient control of $^{29}$Si nuclear spin orientation for specific lattice sites near $^{31}$P donors in silicon crystals at temperatures below 1 K and in high magnetic field of 4.6 T. Excitation of the forbidden electron-nuclear transitions leads to a pattern of narrow holes and peaks in the ESR lines of $^{31}$P. The pattern originates from dynamic polarization the $^{29}$Si nuclear spins near the donors via the solid effect. This method can be used for initialization of qubits based on $^{29}$Si nuclear spins in the all-silicon quantum computer. In comparison, polarization of $^{29}$Si performed by pumping the allowed ESR transitions, did not create any patterns. Instead, a single narrow spectral hole was burnt in the ESR line. The difference is explained by a rapid spin diffusion during the microwave pumping of the allowed transitions.

In spite of both technical and fundamental importance, reversal of a macroscopic magnetization by an electric field (E) has been limitedly realized and remains as one of great challenges. Here, we report the realization of modulation and reversal of large magnetization (M) by E in a multiferroic crystal Ba0.5Sr1.5Zn2(Fe0.92Al0.08)12O22, in which a transverse conical spin state exhibits a remanent M and electric polarization below ~150 K. Upon sweeping E between +- 2 MV/m, M is quasi-linearly varied between +- 2 {\mu}B/f.u., resulting in the M reversal. Moreover, the remanent M shows non-volatile changes of {\Delta}M = +- 0.15 {\mu}B/f.u., depending on the history of the applied electric fields. The large modulation and the non-volatile two-states of M at zero magnetic field are observable up to ~150 K where the transverse conical spin state is stabilized. Nuclear magnetic resonance measurements provide microscopic evidences that the electric field and the magnetic field play an equivalent role, rendering the volume of magnetic domains change accompanied by the domain wall motion. The present findings point to a new pathway for realizing the large magnetization reversal by electric fields at fairly high temperatures., Comment: 26 pages, 7 figures, originally submitted version

We demonstrate that the dynamic nuclear polarization (DNP) of phosphorus donors in silicon can be very effective in a magnetic field of 4.6 T and at temperatures below 1 K. The DNP occurs due to the Overhauser effect following a cross relaxation via the forbidden flip-flop or flip-flip transitions. Nuclear polarization values $P>0.98$ were reached after 20 min of pumping with 0.4 $\mu$W of microwave power. We evaluated that the ratio of hyperfine state populations increased by three orders of magnitude after 2 hours of pumping, and an extremely pure nuclear spin system containing $<10^{-11}$ of the other spin state can be created. An inverted DNP has been obtained by pumping the low field ESR line of P followed by the flip-flip cross relaxation. This transition has much smaller relaxation rate and required substantially longer pumping times. We found that the nuclear polarization dynamics deviates substantially from a simple exponential function. The evolution of the polarization is characterized by two time constants $T^{'}_{ac}\approx$15 s in the beginning, and $T^{"}_{ac}\approx$1100 s for long pumping time. Temperature dependence of the nuclear relaxation rate of $^{31}$P was studied down to 0.75 K, below which the relaxation time became too long to be measured. The nuclear polarization followed a bi-exponential time dependence during relaxation. We suggest that the non-exponential behavior of DNP dynamics and the subsequent relaxation is mediated by the nuclei of $^{29}$Si surrounding $^{31}$P donors, which affect the transition probabilities of the forbidden cross-relaxation processes.

The canting angles and fluctuation of the magnetic ion spins of spinel oxide MnCr${}_2$O${}_4$ were studied by nuclear magnetic resonance (NMR) at low temperatures, which has a collinear ferrimagnetic order below $T_C$ and a ferrimagnetic spiral order below $T_s < T_C$. Contrary to previous reports, only one spin canting angle of Cr ions was observed. The spin canting angles of Mn and Cr ions in the ferrimagnetic spiral obtained at a liquid-He temperature were $43\,^{\circ}$ and $110\,^{\circ}$, respectively. The nuclear spin-spin relaxation was determined by the Suhl-Nakamura interaction at low temperatures but the relaxation rate $T_2^{-1}$ increases rapidly as the temperature approaches $T_s$. This indicates that the fluctuation of the spiral component becomes faster as the temperature increases but not fast enough to leave an averaged hyperfine field to nuclei in the time scale of nuclear spin precession in the ferrimagnetic phase, which is on the order of $10^{-8}$ s. The spiral volume fraction measured for various temperatures reveals that the collinear and the spiral ferrimagnetic phases are mixed below the transition temperature of the spiral order. The temperature hysteresis in the volume fraction implies that this transition has first-order characteristics., Comment: 13 pages, 5 figures

We investigate quantum teleportation through noisy quantum channels by solving analytically and numerically a master equation in the Lindblad form. We calculate the fidelity as a function of decoherence rates and angles of a state to be teleported. It is found that the average fidelity and the range of states to be accurately teleported depend on types of noise acting on quantum channels. If the quantum channels is subject to isotropic noise, the average fidelity decays to 1/2, which is smaller than the best possible value 2/3 obtained only by the classical communication. On the other hand, if the noisy quantum channel is modeled by a single Lindblad operator, the average fidelity is always greater than 2/3., Comment: 6 pages, 5 figures, accepted for publication in Phys. Rev. A

Identifying the Bolch sphere with the Riemann sphere(the extended complex plane), we obtain relations between single qubit unitary operations and M\"{o}bius transformations on the extended complex plane., Comment: 3 pages, 1 figure, revtex, title changed, minor modifications

We consider a quantum circuit in which shift and rotation operations on qubits are performed by swap gates and controlled swap gates. These operations can be useful for quantum computers performing elementary arithmetic operations such as multiplication and a bit-wise comparison of qubits., Comment: 3 pages, 4 figures, revtex

We present a scheme to store unitary operators with self-inverse generators in quantum states and a general circuit to retrieve them with definite success probability. The continuous variable of the operator is stored in a single-qubit state and the information about the kind of the operator is stored in classical states with finite dimension. The probability of successful retrieval is always 1/2 irrespective of the kind of the operator, which is proved to be maximum. In case of failure, the result can be corrected with additional quantum states. The retrieving circuit is almost as simple as that which handles only the single-qubit rotations and CNOT as the basic operations. An interactive way to transfer quantum dynamics, that is, to distribute naturally copy-protected programs for quantum computers is also presented using this scheme., Comment: 4 pages, 3 figures, errors in Eq. (8) and Fig. 3 are fixed, to appear in Phys. Rev. A

We describe a practical method of constructing quantum combinational logic circuits with basic quantum logic gates such as NOT and general $n$-bit Toffoli gates. This method is useful to find the quantum circuits for evaluating logic functions in the form most appropriate for implementation on a given quantum computer. The rules to get the most efficient circuit are utilized best with the aid of a Karnaugh map. It is explained which rules of using a Karnaugh map are changed due to the difference between the quantum and classical logic circuits., Comment: REVTeX, 10 pages, 3 figures

We implemented the refined Deutsch-Jozsa algorithm on a 3-bit nuclear magnetic resonance quantum computer, which is the meaningful test of quantum parallelism because qubits are entangled. All of the balanced and constant functions were realized exactly. The results agree well with theoretical predictions and clearly distinguish the balanced functions from constant functions. Efficient refocusing schemes were proposed for the soft z-pulse and J-coupling and it is proved that the thermal equilibrium state gives the same results as the pure state for this algorithm., Comment: 5 pages, 2 figures, 1 tables, REVTeX

The zero-field $^{139}$La and $^{55}$Mn nuclear magnetic resonances were studied in $\rm La_{0.8}Ca_{0.2}MnO_{3+\delta}$ with different oxygen stoichiometry $\delta$. The signal intensity, peak frequency and line broadening of the $^{139}$La NMR spectrum show that excess oxygens have a tendency to concentrate and establish local ferromagnetic ordering around themselves. These connect the previously existed ferromagnetic clusters embedded in the antiferromagnetic host, resulting in percolative conduction paths. This phase separation is not a charge segregation type, but a electroneutral type. The magnetoresistance peak at the temperature where percolative paths start to form provides a direct evidence that phase separation is one source of colossal magnetoresistance effect., Comment: 4 pages, 5 figures

We present a general method which expresses a unitary operator by the product of operators allowed by the Hamiltonian of spin-1/2 systems. In this method, the generator of an operator is found first, and then the generator is expanded by the base operators of the product operator formalism. Finally, the base operators disallowed by the Hamiltonian, including more than two-body interaction operators, are replaced by allowed ones by the axes transformation and coupling order reduction technique. This method directly provides pulse sequences for the nuclear magnetic resonance quantum computer, and can be generally applied to other systems., Comment: published version, 4 pages, 1 figure, REVTeX