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Quantum Approach to Fast Protein-Folding Time
Li-Hua Lu, You-Quan Li
Chin. Phys. Lett.    2019, 36 (8): 080305 .   DOI: 10.1088/0256-307X/36/8/080305
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In the traditional random-conformational-search model, various hypotheses with a series of meta-stable intermediate states were proposed to resolve the Levinthal paradox in protein-folding time. Here we introduce a quantum strategy to formulate protein folding as a quantum walk on a definite graph, which provides us a general framework without making hypotheses. Evaluating it by the mean of first passage time, we find that the folding time via our quantum approach is much shorter than the one obtained via classical random walks. This idea is expected to evoke more insights for future studies.
Realization of Quantum Maxwell's Demon with Solid-State Spins
W.-B. Wang, X.-Y. Chang, F. Wang, P.-Y. Hou, Y.-Y. Huang, W.-G. Zhang, X.-L. Ouyang, X.-Z. Huang, Z.-Y. Zhang, H.-Y. Wang, L. He, L.-M. Duan
Chin. Phys. Lett.    2018, 35 (4): 040301 .   DOI: 10.1088/0256-307X/35/4/040301
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We report experimental realization of a quantum version of Maxwell's demon using solid state spins where the information acquiring and feedback operations by the demon are achieved through conditional quantum gates. A unique feature of this implementation is that the demon can start in a quantum superposition state or in an entangled state with an ancilla observer. Through quantum state tomography, we measure the entropy in the system, demon, and the ancilla, showing the influence of coherence and entanglement on the result. A quantum implementation of Maxwell's demon adds more controllability to this paradoxical thermal machine and may find applications in quantum thermodynamics involving microscopic systems.
Resonant Quantum Search with Monitor Qubits
Frank Wilczek, Hong-Ye Hu, Biao Wu
Chin. Phys. Lett.    2020, 37 (5): 050304 .   DOI: 10.1088/0256-307X/37/5/050304
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We present an algorithm for the generalized search problem (searching $k$ marked items among $N$ items) based on a continuous Hamiltonian and exploiting resonance. This resonant algorithm has the same time complexity $O(\sqrt{N/k})$ as the Grover algorithm. A natural extension of the algorithm, incorporating auxiliary "monitor" qubits, can determine $k$ precisely, if it is unknown. The time complexity of our counting algorithm is $O(\sqrt{N})$, similar to the best quantum approximate counting algorithm, or better, given appropriate physical resources.
Preservation of Quantum Coherence for Gaussian-State Dynamics in a Non-Markovian Process
Jun Wen, Guan-Qiang Li
Chin. Phys. Lett.    2018, 35 (6): 060301 .   DOI: 10.1088/0256-307X/35/6/060301
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Coherence is a key resource in quantum information science. Exactly understanding and controlling the variation of coherence are vital for implementation in realistic quantum systems. Using $P$-representation of density matrix, we obtain the analytical solution of the master equation for the classical states in the non-Markovian process and investigate the coherent dynamics of Gaussian states. It is found that quantum coherence can be preserved in such a process if the coupling strength between system and environment exceeds a threshold value. We also discuss the characteristic function of the Gaussian states in the non-Markovian process, which provides an inevitable bridge for the control and operation of quantum coherence.
Exact Equivalence between Quantum Adiabatic Algorithm and Quantum Circuit Algorithm
Hongye Yu, Yuliang Huang, Biao Wu
Chin. Phys. Lett.    2018, 35 (11): 110303 .   DOI: 10.1088/0256-307X/35/11/110303
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We present a rigorous proof that quantum circuit algorithm can be transformed into quantum adiabatic algorithm with the exact same time complexity. This means that from a quantum circuit algorithm of $L$ gates we can construct a quantum adiabatic algorithm with time complexity of $O(L)$. Additionally, our construction shows that one may exponentially speed up some quantum adiabatic algorithms by properly choosing an evolution path.
Soliton Molecules and Some Hybrid Solutions for the Nonlinear Schrödinger Equation
Bao Wang, Zhao Zhang, Biao Li
Chin. Phys. Lett.    2020, 37 (3): 030501 .   DOI: 10.1088/0256-307X/37/3/030501
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Based on velocity resonance and Darboux transformation, soliton molecules and hybrid solutions consisting of soliton molecules and smooth positons are derived. Two new interesting results are obtained: the first is that the relationship between soliton molecules and smooth positons is clearly pointed out, and the second is that we find two different interactions between smooth positons called strong interaction and weak interaction, respectively. The strong interaction will only disappear when $t \to \infty$. This strong interaction can also excite some periodic phenomena.
Experimental Hamiltonian Learning of an 11-Qubit Solid-State Quantum Spin Register
P.-Y. Hou, L. He, F. Wang, X.-Z. Huang, W.-G. Zhang, X.-L. Ouyang, X. Wang, W.-Q. Lian, X.-Y. Chang, L.-M. Duan
Chin. Phys. Lett.    2019, 36 (10): 100303 .   DOI: 10.1088/0256-307X/36/10/100303
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Learning the Hamiltonian of a quantum system is indispensable for prediction of the system dynamics and realization of high fidelity quantum gates. However, it is a significant challenge to efficiently characterize the Hamiltonian which has a Hilbert space dimension exponentially growing with the system size. Here, we develop and implement an adaptive method to learn the effective Hamiltonian of an 11-qubit quantum system consisting of one electron spin and ten nuclear spins associated with a single nitrogen-vacancy center in a diamond. We validate the estimated Hamiltonian by designing universal quantum gates based on the learnt Hamiltonian and implementing these gates in the experiment. Our experimental result demonstrates a well-characterized 11-qubit quantum spin register with the ability to test quantum algorithms, and shows our Hamiltonian learning method as a useful tool for characterizing the Hamiltonian of the nodes in a quantum network with solid-state spin qubits.
Phase Transition and Quasinormal Modes for Spherical Black Holes in 5D Gauss–Bonnet Gravity
Ming Zhang, Rui-Hong Yue
Chin. Phys. Lett.    2018, 35 (4): 040401 .   DOI: 10.1088/0256-307X/35/4/040401
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We study the quasinormal modes (QNMs) of massless scalar perturbations to probe the van der Waals like SBH/LBH phase transition of anti-de Sitter black holes in five-dimensional (5D) Gauss–Bonnet gravity. It is found that the signature of this SBH/LBH phase transition is detected when the slopes of the QNMs frequency change drastically and differently in small and large black holes near the critical point. The obtained results further support that the QNMs can be a dynamic probe to investigate the thermodynamic properties in black holes.
Multi-Soliton Solutions for the Coupled Fokas–Lenells System via Riemann–Hilbert Approach
Zhou-Zheng Kang, Tie-Cheng Xia, Xi Ma
Chin. Phys. Lett.    2018, 35 (7): 070201 .   DOI: 10.1088/0256-307X/35/7/070201
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We aim to construct multi-soliton solutions for the coupled Fokas–Lenells system which arises as a model for describing the nonlinear pulse propagation in optical fibers. Starting from the spectral analysis of the Lax pair, a Riemann–Hilbert problem is presented. Then in the framework of the Riemann–Hilbert problem corresponding to the reflectionless case, $N$-soliton solutions to the coupled Fokas–Lenells system are derived explicitly.
A Two-Dimensional Architecture for Fast Large-Scale Trapped-Ion Quantum Computing
Y.-K. Wu  and L.-M. Duan
Chin. Phys. Lett.    2020, 37 (7): 070302 .   DOI: 10.1088/0256-307X/37/7/070302
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Building blocks of quantum computers have been demonstrated in small to intermediate-scale systems. As one of the leading platforms, the trapped ion system has attracted wide attention. A significant challenge in this system is to combine fast high-fidelity gates with scalability and convenience in ion trap fabrication. Here we propose an architecture for large-scale quantum computing with a two-dimensional array of atomic ions trapped at such large distance which is convenient for ion-trap fabrication but usually believed to be unsuitable for quantum computing as the conventional gates would be too slow. Using gate operations far outside of the Lamb–Dicke region, we show that fast and robust entangling gates can be realized in any large ion arrays. The gate operations are intrinsically parallel and robust to thermal noise, which, together with their high speed and scalability of the proposed architecture, makes this approach an attractive one for large-scale quantum computing.
Frozen Quantum Coherence for a Central Two-Qubit System in a Spin-Chain Environment
Yang Yang, An-Min Wang, Lian-Zhen Cao, Jia-Qiang Zhao, Huai-Xin Lu
Chin. Phys. Lett.    2018, 35 (8): 080301 .   DOI: 10.1088/0256-307X/35/8/080301
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We investigate the dynamics of coherence for a central two-qubit system coupled to an $XY$ spin chain with the Dzyaloshinsky–Moriya interaction. It is found that a sudden transition of coherence exists near the critical point in the weak-coupling case, and an oscillatory envelope appears in the strong-coupling case. In both cases the freezing phenomenon of coherence can be found.
Soliton, Breather and Rogue Wave Solutions for the Nonlinear Schrödinger Equation Coupled to a Multiple Self-Induced Transparency System
Xin Wang, Lei Wang
Chin. Phys. Lett.    2018, 35 (3): 030201 .   DOI: 10.1088/0256-307X/35/3/030201
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We derive an $N$-fold Darboux transformation for the nonlinear Schrödinger equation coupled to a multiple self-induced transparency system, which is applicable to optical fiber communications in the erbium-doped medium. The $N$-soliton, $N$-breather and $N$th-order rogue wave solutions in the compact determinant representations are derived using the Darboux transformation and limit technique. Dynamics of such solutions from the first- to second-order ones are shown.
Critical Scaling Behaviors of Entanglement Spectra
Qi-Cheng Tang, Wei Zhu
Chin. Phys. Lett.    2020, 37 (1): 010301 .   DOI: 10.1088/0256-307X/37/1/010301
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We investigate the evolution of entanglement spectra under a global quantum quench from a short-range correlated state to the quantum critical point. Motivated by the conformal mapping, we find that the dynamical entanglement spectra demonstrate distinct finite-size scaling behaviors from the static case. As a prototypical example, we compute real-time dynamics of the entanglement spectra of a one-dimensional transverse-field Ising chain. Numerical simulation confirms that the entanglement spectra scale with the subsystem size $l$ as $\sim$$l^{-1}$ for the dynamical equilibrium state, much faster than $\propto$ $\ln^{-1} l$ for the critical ground state. In particular, as a byproduct, the entanglement spectra at the long time limit faithfully gives universal tower structure of underlying Ising criticality, which shows the emergence of operator-state correspondence in the quantum dynamics.
Measurement of Spin Singlet-Triplet Qubit in Quantum Dots Using Superconducting Resonator
Xing-Yu Zhu, Tao Tu, Ao-Lin Guo, Zong-Quan Zhou, Guang-Can Guo
Chin. Phys. Lett.    2020, 37 (2): 020302 .   DOI: 10.1088/0256-307X/37/2/020302
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The spin qubit in quantum dots is one of the leading platforms for quantum computation. A crucial requirement for scalable quantum information processing is the high efficient measurement. Here we analyze the measurement process of a quantum-dot spin qubit coupled to a superconducting transmission line resonator. Especially, the phase shift of the resonator is sensitive to the spin states and the gate operations. The response of the resonator can be used to measure the spin qubit efficiently, which can be extend to read out the multiple spin qubits in a scalable solid-state quantum processor.
Gravitational Perturbations in Einstein Aether Black Hole Spacetime
Chi-Kun Ding
Chin. Phys. Lett.    2018, 35 (10): 100401 .   DOI: 10.1088/0256-307X/35/10/100401
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We study the gravitational perturbations in Einstein aether black hole spacetime and find that the quasinormal modes (QNMs) of the first kind of aether black hole are similar to that of a Lorentz violation (LV) model, the quantum electrodynamics (QED) extension limit of standard model extension. These similarities between completely different backgrounds may imply that LV in the gravity sector and LV in the matter sector have some connections: damping QNMs more rapidly and prolonging its oscillation period. Compared to the Schwarzschild case, the first kind of black holes have larger damping rates and the second ones have lower damping rates, and they all have smaller real oscillation frequency. These differences could be detected by the new generation of gravitational antennas.
Solitonic Diffusion of Wavepackets in One-Dimensional Bose–Einstein Condensates
Yu Mo, Cong Zhang, Shiping Feng, Shi-Jie Yang
Chin. Phys. Lett.    2019, 36 (12): 120301 .   DOI: 10.1088/0256-307X/36/12/120301
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Solitonic characteristics are revealed in the diffusion process of a hump or a notch wave packet in a one-dimensional Bose–Einstein condensate. By numerically solving the time-dependent Gross–Pitaevskii equation, we find completely different spreading behavior for attractive or repulsive condensates. For the attractive condensate, a series of bright solitons are continuously generated one after another at the wave front and they nearly stay at the positions where they are generated in the whole diffusion process. In contrast, for the repulsive condensate, the initial wave packet splits at the beginning into a series of grey solitons that travel at different velocities. The moving velocity of the grey soliton depends on nonlinear interaction strength, as well as the shape of a particular grey soliton.
Higher-Order Rogue Wave Solutions to a Spatial Discrete Hirota Equation
Jun Yang, Zuo-Nong Zhu
Chin. Phys. Lett.    2018, 35 (9): 090201 .   DOI: 10.1088/0256-307X/35/9/090201
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The higher-order rogue wave (RW) for a spatial discrete Hirota equation is investigated by the generalized (1,$N-1$)-fold Darboux transformation. We obtain the higher-order discrete RW solution to the spatial discrete Hirota equation. The fundamental RWs exhibit different amplitudes and shapes associated with the spectral parameters. The higher-order RWs display triangular patterns and pentagons with different peaks. We show the differences between the RW of the spatially discrete Hirota equation and the discrete nonlinear Schrödinger equation. Using the contour line method, we study the localization characters including the length, width, and area of the first-order RWs of the spatially discrete Hirota equation.
Period-Doubled Bloch States in a Bose–Einstein Condensate
Bao-Guo Yang, Peng-Ju Tang, Xin-Xin Guo, Xu-Zong Chen, Biao Wu, Xiao-Ji Zhou
Chin. Phys. Lett.    2018, 35 (7): 070301 .   DOI: 10.1088/0256-307X/35/7/070301
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We study systematically the period-doubled Bloch states for a weakly interacting Bose–Einstein condensate in a one-dimensional optical lattice. This kind of state is of form $\psi_k=e^{ikx}\phi_k(x)$, where $\phi_k(x)$ is of a period twice the optical lattice constant. Our numerical results show how these nonlinear period-doubled states grow out of linear period-doubled states at a quarter away from the Brillouin zone center as the repulsive interatomic interaction increases. This is corroborated by our analytical results. We find that all nonlinear period-doubled Bloch states have both Landau instability and dynamical instability.
Coherent Coupling between Microwave and Optical Fields via Cold Atoms
Zhen-Tao Liang, Qing-Xian Lv, Shan-Chao Zhang, Wei-Tao Wu, Yan-Xiong Du, Hui Yan, Shi-Liang Zhu
Chin. Phys. Lett.    2019, 36 (8): 080301 .   DOI: 10.1088/0256-307X/36/8/080301
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We demonstrate a long-coherent-time coupling between microwave and optical fields through cold atomic ensembles. The phase information of the microwave field is stored in a coherent superposition state of a cold atomic ensemble and is then read out by two optical fields after 12 ms. A similar operation of mapping the phase of optical fields into a cold atomic ensemble and then retrieving by microwave is also demonstrated. These studies demonstrate that long-coherent-time cold atomic ensembles could resonantly couple with microwave and optical fields simultaneously, which paves the way for realizing high-efficiency, high-bandwidth, and noiseless atomic quantum converters.
Soliton Molecules, Asymmetric Solitons and Hybrid Solutions for (2+1)-Dimensional Fifth-Order KdV Equation
Zhao Zhang, Shu-Xin Yang, Biao Li
Chin. Phys. Lett.    2019, 36 (12): 120501 .   DOI: 10.1088/0256-307X/36/12/120501
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Soliton molecules were first discovered in optical systems and are currently a hot topic of research. We obtain soliton molecules of the (2+1)-dimensional fifth-order KdV system under a new resonance condition called velocity resonance in theory. On the basis of soliton molecules, asymmetric solitons can be obtained by selecting appropriate parameters. Based on the $N$-soliton solution, we obtain hybrid solutions consisting of soliton molecules, lump waves and breather waves by partial velocity resonance and partial long wave limits. Soliton molecules, and some types of special soliton resonance solutions, are stable under the meaning that the interactions among soliton molecules are elastic. Both soliton molecules and asymmetric solitons obtained may be observed in fluid systems because the fifth-order KdV equation describes the ion-acoustic waves in plasmas, shallow water waves in channels and oceans.
The Search for the Quantum Spin Liquid in Kagome Antiferromagnets
J.-J. Wen, Y. S. Lee
Chin. Phys. Lett.    2019, 36 (5): 050101 .   DOI: 10.1088/0256-307X/36/5/050101
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Solutions to Nonlocal Integrable Discrete Nonlinear Schrödinger Equations via Reduction
Ya-Hong Hu, Jun-Chao Chen
Chin. Phys. Lett.    2018, 35 (11): 110201 .   DOI: 10.1088/0256-307X/35/11/110201
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Solutions to local and nonlocal integrable discrete nonlinear Schrödinger (IDNLS) equations are studied via reduction on the bilinear form. It is shown that these solutions to IDNLS equations can be expressed in terms of the single Casorati determinant under different constraint conditions.
Two-Photon Interference Constructed by Two Hong–Ou–Mandel Effects in One Mach-Zehnder Interferometer
Rui Liu, Ling-Jun Kong, Zhou-Xiang Wang, Yu Si, Wen-Rong Qi, Shuang-Yin Huang, Chenghou Tu, Yongnan Li, Hui-Tian Wang
Chin. Phys. Lett.    2018, 35 (9): 090303 .   DOI: 10.1088/0256-307X/35/9/090303
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We present a two-photon interference experiment in a modified Mach-Zehnder (MZ) interferometer in which two Hong–Ou–Mandel effects occur in tandem and construct superposed two-photon states. The signal photons pass both the arms of the MZ interferometer while the idler photons pass one arm only. Interestingly, the probability of the idler photons emerging from any output port still shows a sine oscillation with the two-photon phase difference and it can be characterized only by the indistinguishability of the two-photon amplitudes. We also observe a two-photon interference pattern with a period being equal to the wavelength of the parametric photons instead of the two-photon photonic de Broglie wavelength due to the presence of two-photon phase difference, in particular, with complementary probabilities of finding the two-photon pairs in two output ports. The abundant observations can facilitate a more comprehensive understanding of the two-photon interference.
Demonstration of a Sub-Sampling Phase Lock Loop Based Microwave Source for Reducing Dick Effect in Atomic Clocks
Wen-Bing Li, Qiang Hao, Yuan-Bo Du, Shao-Qing Huang, Peter Yun, Ze-Huang Lu
Chin. Phys. Lett.    2019, 36 (7): 070601 .   DOI: 10.1088/0256-307X/36/7/070601
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We demonstrate a simple scheme of 6.835 GHz microwave source based on the sub-sampling phase lock loop (PLL). A dielectric resonant oscillator of 6.8 GHz is directly phase locked to an ultra-low phase noise 100 MHz oven controlled crystal oscillator (OCXO) utilizing the sub-sampling PLL. Then the 6.8 GHz is mixed with 35 MHz from an direct digital synthesizer (DDS) which is also referenced to the 100 MHZ OCXO to generate the final 6.835 GHz signal. Benefiting from the sub-sampling PLL, the processes of frequency multiplication, which are usually necessary in the development of a microwave source, are greatly simplified. The architecture of the microwave source is pretty simple. Correspondingly, its power consumption and cost are low. The absolute phase noises of the 6.835 GHz output signal are $-$47 dBc/Hz, $-$77 dBc/Hz, $-$104 dBc/Hz and $-$121 dBc/Hz at 1 Hz, 10 Hz, 100 Hz and 1 kHz offset frequencies, respectively. The frequency stability limited by the phase noise through the Dick effect is theoretically estimated to be better than $5.0 \times 10^{-14}\tau^{1/2}$ when it is used as the local oscillator of the Rb atomic clocks. This low phase noise microwave source can also be used in other experiments of precision measurement physics.
Observation of $^1\!S_0$$\rightarrow$$^3\!P_0$ Transition of a $^{40}$Ca$^+$-$^{27}$Al$^+$ Quantum Logic Clock
Si-Jia Chao, Kai-Feng Cui, Shao-Mao Wang, Jian Cao, Hua-Lin Shu, Xue-Ren Huang
Chin. Phys. Lett.    2019, 36 (12): 120601 .   DOI: 10.1088/0256-307X/36/12/120601
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We report the realization of quantum logic spectroscopy on the $^1\!S_0\rightarrow {}^3\!P_0$ clock transition of a single $^{27}$Al$^+$ ion. This ion is trapped together with a $^{40}$Ca$^+$ ion in a linear Paul trap, coupled by Coulomb repulsion, which provides sympathetic Doppler laser cooling and also the means for internal state detection of the clock state of the $^{27}$Al$^+$ ion. A repetitive quantum nondemolition measurement is performed to improve the fidelity of state detection. These techniques are applied to obtain clock spectroscopy at approximately 45 Hz. We also perform the preliminary locking on the $^1\!S_0\rightarrow {}^3\!P_0$ clock transition. Our work is a fundamental step that is necessary toward obtaining an ultra-precision quantum logic clock based on $^{40}$Ca$^+$-$^{27}$Al$^+$ ions.
An Atomic Magnetometer with Spin-Projection Noise Proportional to $\sqrt{{T_2}}$
Hai-Feng Dong, Xiao-Fei Wang, Ji-Min Li, Jing-Ling Chen, Yuan Ren
Chin. Phys. Lett.    2019, 36 (2): 020701 .   DOI: 10.1088/0256-307X/36/2/020701
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There is a common sense view for atomic magnetometers that their spin-projection-noises (SPNs) are inversely proportional to $\sqrt{{T_2}}$, where $T_2$ is the transverse relaxation time. We analyze the current atomic magnetometer types and give a counter-example of this common sense, which is the all-optical spin precession modulated three-axis atomic magnetometer proposed by our group in 2015. Unlike the other atomic magnetometers, the SPN of this kind of atomic magnetometers is proportional to $\sqrt{{T_2}}$ due to the fact that the scale factor between $P_x$ and $B$ can be unrelated to the transverse relaxation time $T_2$. We demonstrate this irrelevance experimentally and analyze the SPN theoretically. Using short-pulse ultra-high power laser to fully polarize the atoms, the phenomenon that SPN decreases with $T_2$ may also be demonstrated experimentally and a new tool for researching SPN in atomic magnetometers may be realized.
Imaginary Time Crystal of Thermal Quantum Matter
Zi Cai, Yizhen Huang, W. Vincent Liu
Chin. Phys. Lett.    2020, 37 (5): 050503 .   DOI: 10.1088/0256-307X/37/5/050503
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Temperature is a fundamental thermodynamic variable for matter. Physical observables are often found to either increase or decrease with it, or show a non-monotonic dependence with peaks signaling underlying phase transitions or anomalies. Statistical field theory has established connection between temperature and time: a quantum ensemble with inverse temperature $\beta$ is formally equivalent to a dynamic system evolving along an imaginary time from 0 to $i\beta$ in the space one dimension higher. Here we report that a gas of hard-core bosons interacting with a thermal bath manifests an unexpected temperature-periodic oscillation of its macroscopic observables, arising from the microscopic origin of space-time locked translational symmetry breaking and crystalline ordering. Such a temperature crystal, supported by quantum Monte Carlo simulation, generalizes the concept of purely spatial density-wave order to the imaginary time axis for Euclidean action.
Renormalization of Tripartite Entanglement in Spin Systems with Dzyaloshinskii–Moriya Interaction
Meng Qin, Li Wang, Bili Wang, Xiao Wang, Zhong Bai, Yanbiao Li
Chin. Phys. Lett.    2018, 35 (10): 100301 .   DOI: 10.1088/0256-307X/35/10/100301
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Quantum entanglement represents a fundamental feature of quantum many-body systems. We combine tripartite entanglement with quantum renormalization group theory to study the quantum critical phenomena. The Ising model and the Heisenberg $XXZ$ model in the presence of the Dzyaloshinskii–Moriya interaction are adopted as the research objects. We identify that the tripartite entanglement can signal the critical point. The derivative of tripartite entanglement shows singularity as the spin chain size increases. Furthermore, the intuitive scaling behavior of the system selected is studied and the result allows us to precisely quantify the correlation exponent by utilizing the power law.
Dynamical Evolution of an Effective Two-Level System with $\mathcal{PT}$ Symmetry
Lei Du, Zhihao Xu, Chuanhao Yin, Liping Guo
Chin. Phys. Lett.    2018, 35 (5): 050301 .   DOI: 10.1088/0256-307X/35/5/050301
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We investigate the dynamics of parity- and time-reversal ($\mathcal{PT}$) symmetric two-energy-level atoms in the presence of two optical and one radio-frequency fields. The strength and relative phase of fields can drive the system from the unbroken to the broken $\mathcal{PT}$ symmetric regions. Compared with the Hermitian model, Rabi-type oscillation is still observed, and the oscillation characteristics are also adjusted by the strength and relative phase in the region of the unbroken $\mathcal{PT}$ symmetry. At the exception point, the oscillation breaks down. To better understand the underlying properties we study the effective Bloch dynamics and find that the emergence of the $z$ components of the fixed points is the feature of the $\mathcal{PT}$ symmetry breaking and the projections in the $x$–$y$ plane can be controlled with high flexibility compared with the standard two-level system with the $\mathcal{PT}$ symmetry. It helps to study the dynamic behavior of the complex $\mathcal{PT}$ symmetric model.
Impact of Distribution Fairness Degree and Entanglement Degree on Cooperation
Xin Zhao, Bo-Yang Liu, Ying Yi, Hong-Yi Dai, Ming Zhang
Chin. Phys. Lett.    2018, 35 (3): 030202 .   DOI: 10.1088/0256-307X/35/3/030202
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We explore the impact of distributional fairness degree and entanglement degree on the cooperation between different players by investigating a modified prisoner's dilemma game. We not only introduce a new concept of distributional fairness degree, but also obtain the cooperation conditions for overcoming dilemma in terms of fairness and entanglement inequalities. It is demonstrated that distributional fairness can be of fundamental importance to promote cooperation with the help of quantum entanglement.
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