In contrast to the solutions of applied mathematics to Zeno’s paradoxes, I focus on the concept of motion and show that, by distinguishing two different forms of motion, Zeno’s apparent paradoxes are not paradoxical...In contrast to the solutions of applied mathematics to Zeno’s paradoxes, I focus on the concept of motion and show that, by distinguishing two different forms of motion, Zeno’s apparent paradoxes are not paradoxical at all. Zeno’s paradoxes indirectly prove that distances are not composed of extensionless points and, in general, that a higher dimension cannot be completely composed of lower ones. Conversely, lower dimensions can be understood as special cases of higher dimensions. To illustrate this approach, I consider Cantor’s only apparent proof that the real numbers are uncountable. However, his widely accepted indirect proof has the disadvantage that it depends on whether there is another way to make the real numbers countable. Cantor rightly assumes that there can be no smallest number between 0 and 1, and therefore no beginning of counting. For this reason he arbitrarily lists the real numbers in order to show with his diagonal method that this list can never be complete. The situation is different if we start with the largest number between 0 and 1 (0.999…) and use the method of an inverted triangle, which can be understood as a special fractal form. Here we can construct a vertical and a horizontal stratification with which it is actually possible to construct all real numbers between 0 and 1 without exception. Each column is infinite, and each number in that column is the starting point of a new triangle, while each row is finite. Even in a simple sine curve, we experience finiteness with respect to the y-axis and infinity with respect to the x-axis. The first parts of this article show that Zeno’s assumptions contradict the concept of motion as such, so it is not surprising that this misconstruction leads to contradictions. In the last part, I discuss Cantor’s diagonal method and explain the method of an inverted triangle that is internally structured like a fractal by repeating this inverted triangle at each column. The consequence is that we encounter two very different methods of count展开更多
We provide a general dynamical approach for the quantum Zeno and anti-Zeno effects in an open quantum system under repeated non-demolition measurements. In our approach the repeated measurements are described by a gen...We provide a general dynamical approach for the quantum Zeno and anti-Zeno effects in an open quantum system under repeated non-demolition measurements. In our approach the repeated measurements are described by a general dynamical model without the wave function collapse postulation. Based on that model, we further study both the short-time and long-time evolutions of the open quantum system under repeated non-demolition measurements, and derive the measurement-modified decay rates of the excited state. In the cases with frequent ideal measurements at zero-temperature, we re-obtain the same decay rate as that from the wave function collapse postulation （Nature, 2000, 405： 546）. The correction to the ideal decay rate is also obtained under the non-ideal measurements. Especially, we find that the quantum Zeno and anti-Zeno effects are possibly enhanced by the non-ideal natures of measurements. For the open system under measurements with arbitrary period, we generally derive the rate equation for the long-time evolution for the cases with arbitrary temperature and noise spectrum, and show that in the long-time evolution the noise spectrum is effectively tuned by the repeated measurements. Our approach is also able to describe the quantum Zeno and anti-Zeno effects given by the phase modulation pulses, as well as the relevant quantum control schemes.展开更多
In this work,a novel gradient descent method based on event-triggered strategy has been proposed,which involves integer and fractional order iteration.Firstly,the convergence of integer order iterative optimization me...In this work,a novel gradient descent method based on event-triggered strategy has been proposed,which involves integer and fractional order iteration.Firstly,the convergence of integer order iterative optimization method and the stability of its associated system with integrator dynamics are linked.Based on this result,a fractional order iteration approach has been developed by modelling the system with fractional order dynamics.Secondly,to reduce the comsumption of computation,a feedback based event-triggered mechanism has been introduced to the gradient descent method.The convergence of this new event-triggered optimization algorithm is guaranteed by using a Lyapunov method,and Zeno behavior is proved to be avoided simultaneously.Lastly,the effectiveness and advantages of the proposed algorithms are verified by numerical simulations.展开更多
Imaginary potentials such as V(x)=−iσ1Ω(x)(withσ>0 a constant,Ωa subset of 3-space,and 1Ωits characteristic function)have been used in quantum mechanics as models of a detector.They represent the effect of a‘...Imaginary potentials such as V(x)=−iσ1Ω(x)(withσ>0 a constant,Ωa subset of 3-space,and 1Ωits characteristic function)have been used in quantum mechanics as models of a detector.They represent the effect of a‘soft’detector that takes a while to notice a particle in the detector volumeΩ.In order to model a‘hard’detector(i.e.one that registers a particle as soon as it entersΩ),one may think of taking the limitσ→∞of increasing detector strengthσ.However,as pointed out by Allcock,in this limit the particle never entersΩ;its wave function gets reflected at the boundary∂ΩofΩin the same way as by a Dirichlet boundary condition on∂Ω.This phenomenon,a cousin of the‘quantum Zeno effect,’might suggest that a hard detector is mathematically impossible.Nevertheless,a mathematical description of a hard detector has recently been put forward in the form of the‘absorbing boundary rule’involving an absorbing boundary condition on the detecting surface∂Ω.We show here that in a suitable(non-obvious)limit,the imaginary potential V yields a non-trivial distribution of detection time and place in agreement with the absorbing boundary rule.That is,a hard detector can be obtained as a limit,but it is a different limit than Allcock considered.展开更多
In this paper, we study a quantum anti-Zeno effect （QAZE） purely induced by repetitive measurements for an artificial atom interacting with a structured bath. This bath can be artificially realized with coupled reso...In this paper, we study a quantum anti-Zeno effect （QAZE） purely induced by repetitive measurements for an artificial atom interacting with a structured bath. This bath can be artificially realized with coupled resonators in one dimension and possesses photonic band structure like Bloeh electron in a periodic potential. In the presence of repetitive measurements, the pure QAZE is discovered as the observable decay is not negligible even for the atomic energy level spacing outside of the energy band of the artificial bath. If there were no measurements, the decay would not happen outside of the band. In this sense, the enhanced decay is completely induced by measurements through the relaxation channels provided by the bath. Besides, we also discuss the controversial golden rule decay rates originated from the van Hove＇s singularities and the effects of the counter-rotating terms.展开更多
We study the contain men t cont rol problem for high-order het erogeneous nonlinear multi-age nt systems under distributed event-triggered schemes.To achieve the containment control objective and reduce communication ...We study the contain men t cont rol problem for high-order het erogeneous nonlinear multi-age nt systems under distributed event-triggered schemes.To achieve the containment control objective and reduce communication consumption among agents,a distributed event-triggered control scheme is proposed by applying the backstepping method,Lyapunov functional approach,and neural networks.Then,the results are extended to the self-triggered control case to avoid continuous monitoring of state errors.The developed protocols and triggered rules ensure that the output for each follower converges to the convex hull spanned by multi-leader signals within a bounded error.In addition,no agent exhibits Zeno behavior.Two numerical simulations are finally presen ted to verify the correctness of the obtained results.展开更多
Guiding of waves between parallel absorbing walls is considered. The principal mode is constructed;its absorption is estimated. The agreement with previous results about reflection of waves from absorbing walls is dis...Guiding of waves between parallel absorbing walls is considered. The principal mode is constructed;its absorption is estimated. The agreement with previous results about reflection of waves from absorbing walls is discussed. Roughly, the effective absorption of the principal mode is proportional the minus third power of the distance between walls, minus 1.5 d power of the wavenumber and minus 0.5 power of the local absorption of the wave in the wall. This estimate is suggested as hint for the design of the atomic waveguides, and also as tool for optimization of attenuation of the amplified spontaneous emission (and suppression of parasitic oscillations) in high power lasers.展开更多
Following a recent proposal by Dhar et al （2006 Phys. Rev. Lett. 96 100405）, we demonstrate experimentally the preservation of quantum states in a two-qubit system based on a super-Zeno effect using liquid-state nuc...Following a recent proposal by Dhar et al （2006 Phys. Rev. Lett. 96 100405）, we demonstrate experimentally the preservation of quantum states in a two-qubit system based on a super-Zeno effect using liquid-state nuclear magnetic resonance techniques. Using inverting radiofrequency pulses and delicately selecting time intervals between two pulses, we suppress the effect of decoherence of quantum states. We observe that preservation of the quantum state ｜11〉 with the super-Zeno effect is three times more efficient than the ordinary one with the standard Zeno effect.展开更多
The Zeno time has been calculated for a metastable two-level atom tunneling through a interacting thermal magnetic field. The process of weak measurement has been utilized for the estimation of the timescale. Zeno tim...The Zeno time has been calculated for a metastable two-level atom tunneling through a interacting thermal magnetic field. The process of weak measurement has been utilized for the estimation of the timescale. Zeno time has been shown to be temperature dependent. From the calculation it is evident that the Zeno time decreases with the increase of temperature. Moreover, the result restricts the Zeno time to a maximum limiting value, irrespective of how frequent the measurement process is.展开更多
The measurement-result-conditioned evolution of a system(e.g., an atom) with spontaneous emissions of photons is described by the quantum trajectory(QT) theory. In this work we generalize the associated QT theory from...The measurement-result-conditioned evolution of a system(e.g., an atom) with spontaneous emissions of photons is described by the quantum trajectory(QT) theory. In this work we generalize the associated QT theory from an infinitely wide bandwidth Markovian environment to the finite bandwidth non-Markovian environment. In particular, we generalize the treatment for an arbitrary spectrum, which is not restricted by the specific Lorentzian case. We rigorously prove the general existence of a perfect scaling behavior jointly defined by the bandwidth of the environment and the time interval between successive photon detections.For a couple of examples, we obtain analytic results to facilitate the QT simulations based on the Monte-Carlo algorithm. For the case where the analytical result is not available, a numerical scheme is proposed for practical simulations.展开更多
In the context of continuous piecewise affine dynamical systems and affine complementarity systems with inputs, we study the existence of Zeno behavior, i.e., infinite number of mode transitions in a finite-length tim...In the context of continuous piecewise affine dynamical systems and affine complementarity systems with inputs, we study the existence of Zeno behavior, i.e., infinite number of mode transitions in a finite-length time interval, in this paper. The main result reveals that continuous piecewise affine dynamical systems with piecewise real-analytic inputs do not exhibit Zeno behavior. Applied the achieved result to affine complementarity systems with inputs, we also obtained a similar conclusion. A direct benefit of the main result is that one can apply smooth ordinary differential equations theory in a local manner for the analysis of continuous piecewise affine dynamical systems with inputs.展开更多
After a brief reference to the quantum Zeno effect, a quantum Zeno paradox is formulated. Our starting point is the usual version of Time Dependent Perturbation Theory. Although this theory is supposed to account for ...After a brief reference to the quantum Zeno effect, a quantum Zeno paradox is formulated. Our starting point is the usual version of Time Dependent Perturbation Theory. Although this theory is supposed to account for transitions between stationary states, we are led to conclude that such transitions cannot occur. Paraphrasing Zeno, they are nothing but illusions. Two solutions to the paradox are introduced. The first as a straightforward application of the postulates of Orthodox Quantum Mechanics;the other is derived from a Spontaneous Projection Approach to quantum mechanics previously formulated. Similarities and differences between both solutions are highlighted. A comparison between the two versions of quantum mechanics, supporting their corresponding solutions to the paradox, shines a new light on quantum weirdness. It is shown, in particular, that the solution obtained in the framework of Orthodox Quantum Mechanics is defective.展开更多
We propose a new mechanism, parallel quantum Zeno dynamics, to dissipatively prepare all Bell entangled states of the twoqubit system in the context of cavity quantum electrodynamics. This mechanism can provide two tr...We propose a new mechanism, parallel quantum Zeno dynamics, to dissipatively prepare all Bell entangled states of the twoqubit system in the context of cavity quantum electrodynamics. This mechanism can provide two transition channels between ground states and two different dark states simultaneously, which efficiently speeds up the stabilization of the entanglement and suppresses the adverse influence of surrounding environments. In addition, there is no need for the initialization of quantum states and the Clauser-Horne-Shimony-Holt inequality can be violated in a finite temperature bath. The experimental feasibility is also studied by the state-of-the-art technique and a high fidelity about 99% can be achieved.展开更多
The study of the polaron of an open quantum system plays an important role in verifying the effectiveness of an approximate many-body theory and predicting novel quantum phenomena in open quantum systems. In a pioneer...The study of the polaron of an open quantum system plays an important role in verifying the effectiveness of an approximate many-body theory and predicting novel quantum phenomena in open quantum systems. In a pioneering work, Piazza et al.(2021) proposed a Fermi-polaron scheme with a lossy impurity, which exhibits a novel long-lived attractive polaron branch in the quantum Zeno limit. However, we have encountered a counterpart problem in which an impurity interacting with an open quantum bath scatters exciting polarons, which is what we focus on. In this work, we determine through analytical research the molecular state under the two limits of vanishingly small and infinitely large dissipation intensities as well as the reason why the dissipation range leads to a decrease in the gap between the molecular state and the molecule-hole continuum in the former case.The spectrum functions of molecular and polaron states with different dissipation ranges and loss rates are investigated. We find the spectral signals of molecular and polaron states will first diffuse and then revive as the dissipation increases. Moreover, we show that the attractive and repulsive polarons respond differently to an increasing dissipation range in our model. Finally, we exhibit the polaron energy, residue, effective mass, and two-body decay for mass-balanced and imbalanced systems. Our results might be useful for cold-atom experiments on open quantum systems.展开更多
Recently we proposed “a new interpretation of quantum mechanics (called quantum and classical measurement theory)” in this journal (JQIS: Vol. 1, No. 2), which was characterized as the metaphysical and linguistic tu...Recently we proposed “a new interpretation of quantum mechanics (called quantum and classical measurement theory)” in this journal (JQIS: Vol. 1, No. 2), which was characterized as the metaphysical and linguistic turn of quantum mechanics. This turn from physics to language does not only realize the remarkable extension of quantum mechanics but also yield the quantum mechanical world view (i.e., the philosophy of quantum mechanics). And thus, the turn urges us to dream that traditional philosophies (i.e., Parmenides, Plato, Aristotle, Descartes, John Locke, Berkeley, Hume, Kant, Saussure, Wittgenstein, etc.) can be understood in the quantum mechanical world view. This dream will be challenged in this paper. We, of course, know that most scientists are skeptical to philosophy. Still, we can expect that readers find a good linguistic philosophy (i.e. philosophy of language) in quantum mechanics.展开更多
We propose a scheme to achieve nuclear–nuclear indirect interactions mediated by a mechanically driven nitrogen-vacancy(NV)center in a diamond.Here we demonstrate twoqubit entangling gates and quantum-state transfer ...We propose a scheme to achieve nuclear–nuclear indirect interactions mediated by a mechanically driven nitrogen-vacancy(NV)center in a diamond.Here we demonstrate twoqubit entangling gates and quantum-state transfer between two carbon nuclei.When the dipole–dipole interaction strength is much larger than the driving field strength,the scheme is robust against decoherence caused by coupling between the NV center(nuclear spins)and the environment.Conveniently,precise control of dipole coupling is not required so this scheme is insensitive to fluctuating positions of the nuclear spins and the NV center.Our scheme provides a general blueprint for multi-nuclear-spin gates and for multi-party communication.展开更多
Based on the quantum Zeno dynamics,we propose a two-qubit non-geometric conditional phase gate between two nitrogen-vacancy centers coupled to a whispering-gallery mode cavity.The varying phases design of periodic las...Based on the quantum Zeno dynamics,we propose a two-qubit non-geometric conditional phase gate between two nitrogen-vacancy centers coupled to a whispering-gallery mode cavity.The varying phases design of periodic laser can be used for realizing non-geometric conditional phase gate,and the cavity mode is virtually excited during the gate operation.Thus,the fidelity of the gate operation is insensitive to cavity decay and the fluctuation of the preset laser intensity.The numerical simulation with a realistic set of experimental parameters shows that the gate fidelity 0.987 can be within reached in the near future.展开更多
Our main aim is to prove a more general version of the quantum Zeno effect. Then we discuss some examples of the quantum Zeno effect. Furthermore, we discuss a possibility that based on the quantum Zeno effect and cer...Our main aim is to prove a more general version of the quantum Zeno effect. Then we discuss some examples of the quantum Zeno effect. Furthermore, we discuss a possibility that based on the quantum Zeno effect and certain experiments one could check whether, from the statistical point of view, a concrete system behaves like a quantum system. The more general version of quantum Zeno effect can be helpful to prove that the brain acts like in a quantum system. The proof of our main result is based on certain formulas describing probability distributions of time series related to quantum measurements.展开更多
文摘In contrast to the solutions of applied mathematics to Zeno’s paradoxes, I focus on the concept of motion and show that, by distinguishing two different forms of motion, Zeno’s apparent paradoxes are not paradoxical at all. Zeno’s paradoxes indirectly prove that distances are not composed of extensionless points and, in general, that a higher dimension cannot be completely composed of lower ones. Conversely, lower dimensions can be understood as special cases of higher dimensions. To illustrate this approach, I consider Cantor’s only apparent proof that the real numbers are uncountable. However, his widely accepted indirect proof has the disadvantage that it depends on whether there is another way to make the real numbers countable. Cantor rightly assumes that there can be no smallest number between 0 and 1, and therefore no beginning of counting. For this reason he arbitrarily lists the real numbers in order to show with his diagonal method that this list can never be complete. The situation is different if we start with the largest number between 0 and 1 (0.999…) and use the method of an inverted triangle, which can be understood as a special fractal form. Here we can construct a vertical and a horizontal stratification with which it is actually possible to construct all real numbers between 0 and 1 without exception. Each column is infinite, and each number in that column is the starting point of a new triangle, while each row is finite. Even in a simple sine curve, we experience finiteness with respect to the y-axis and infinity with respect to the x-axis. The first parts of this article show that Zeno’s assumptions contradict the concept of motion as such, so it is not surprising that this misconstruction leads to contradictions. In the last part, I discuss Cantor’s diagonal method and explain the method of an inverted triangle that is internally structured like a fractal by repeating this inverted triangle at each column. The consequence is that we encounter two very different methods of count
基金supported by the National Natural Science Foundation of China(Grant Nos.11074305,10935010,11074261 and 11121403)the National Basic Research Program of China(Grant Nos.2012CB922104 and 2014CB921402)
文摘We provide a general dynamical approach for the quantum Zeno and anti-Zeno effects in an open quantum system under repeated non-demolition measurements. In our approach the repeated measurements are described by a general dynamical model without the wave function collapse postulation. Based on that model, we further study both the short-time and long-time evolutions of the open quantum system under repeated non-demolition measurements, and derive the measurement-modified decay rates of the excited state. In the cases with frequent ideal measurements at zero-temperature, we re-obtain the same decay rate as that from the wave function collapse postulation （Nature, 2000, 405： 546）. The correction to the ideal decay rate is also obtained under the non-ideal measurements. Especially, we find that the quantum Zeno and anti-Zeno effects are possibly enhanced by the non-ideal natures of measurements. For the open system under measurements with arbitrary period, we generally derive the rate equation for the long-time evolution for the cases with arbitrary temperature and noise spectrum, and show that in the long-time evolution the noise spectrum is effectively tuned by the repeated measurements. Our approach is also able to describe the quantum Zeno and anti-Zeno effects given by the phase modulation pulses, as well as the relevant quantum control schemes.
基金supported by the National Natural Science Foundation of China under Grant No.61973291。
文摘In this work,a novel gradient descent method based on event-triggered strategy has been proposed,which involves integer and fractional order iteration.Firstly,the convergence of integer order iterative optimization method and the stability of its associated system with integrator dynamics are linked.Based on this result,a fractional order iteration approach has been developed by modelling the system with fractional order dynamics.Secondly,to reduce the comsumption of computation,a feedback based event-triggered mechanism has been introduced to the gradient descent method.The convergence of this new event-triggered optimization algorithm is guaranteed by using a Lyapunov method,and Zeno behavior is proved to be avoided simultaneously.Lastly,the effectiveness and advantages of the proposed algorithms are verified by numerical simulations.
文摘Imaginary potentials such as V(x)=−iσ1Ω(x)(withσ>0 a constant,Ωa subset of 3-space,and 1Ωits characteristic function)have been used in quantum mechanics as models of a detector.They represent the effect of a‘soft’detector that takes a while to notice a particle in the detector volumeΩ.In order to model a‘hard’detector(i.e.one that registers a particle as soon as it entersΩ),one may think of taking the limitσ→∞of increasing detector strengthσ.However,as pointed out by Allcock,in this limit the particle never entersΩ;its wave function gets reflected at the boundary∂ΩofΩin the same way as by a Dirichlet boundary condition on∂Ω.This phenomenon,a cousin of the‘quantum Zeno effect,’might suggest that a hard detector is mathematically impossible.Nevertheless,a mathematical description of a hard detector has recently been put forward in the form of the‘absorbing boundary rule’involving an absorbing boundary condition on the detecting surface∂Ω.We show here that in a suitable(non-obvious)limit,the imaginary potential V yields a non-trivial distribution of detection time and place in agreement with the absorbing boundary rule.That is,a hard detector can be obtained as a limit,but it is a different limit than Allcock considered.
基金Supported by the Natural Science Foundation of China under Grant Nos.10974209 and 10935010 the National 973 Program under Grant No.2006CB921205China Postdoctoral Science Foundation under Grant No.20100470584
文摘In this paper, we study a quantum anti-Zeno effect （QAZE） purely induced by repetitive measurements for an artificial atom interacting with a structured bath. This bath can be artificially realized with coupled resonators in one dimension and possesses photonic band structure like Bloeh electron in a periodic potential. In the presence of repetitive measurements, the pure QAZE is discovered as the observable decay is not negligible even for the atomic energy level spacing outside of the energy band of the artificial bath. If there were no measurements, the decay would not happen outside of the band. In this sense, the enhanced decay is completely induced by measurements through the relaxation channels provided by the bath. Besides, we also discuss the controversial golden rule decay rates originated from the van Hove＇s singularities and the effects of the counter-rotating terms.
基金Project supported by the National Natural Science Foundation of China(Nos.61873128 and 61673219)the Jiangsu Key Research and Development Plan,China(No.BE2018004-3)。
文摘We study the contain men t cont rol problem for high-order het erogeneous nonlinear multi-age nt systems under distributed event-triggered schemes.To achieve the containment control objective and reduce communication consumption among agents,a distributed event-triggered control scheme is proposed by applying the backstepping method,Lyapunov functional approach,and neural networks.Then,the results are extended to the self-triggered control case to avoid continuous monitoring of state errors.The developed protocols and triggered rules ensure that the output for each follower converges to the convex hull spanned by multi-leader signals within a bounded error.In addition,no agent exhibits Zeno behavior.Two numerical simulations are finally presen ted to verify the correctness of the obtained results.
文摘Guiding of waves between parallel absorbing walls is considered. The principal mode is constructed;its absorption is estimated. The agreement with previous results about reflection of waves from absorbing walls is discussed. Roughly, the effective absorption of the principal mode is proportional the minus third power of the distance between walls, minus 1.5 d power of the wavenumber and minus 0.5 power of the local absorption of the wave in the wall. This estimate is suggested as hint for the design of the atomic waveguides, and also as tool for optimization of attenuation of the amplified spontaneous emission (and suppression of parasitic oscillations) in high power lasers.
基金Project supported by the National Natural Science Foundation of China (Grant Nos 10374103, 10574143 and 10874206)the National Key Basic Research Program of China (Grant No 2006CB921203)
文摘Following a recent proposal by Dhar et al （2006 Phys. Rev. Lett. 96 100405）, we demonstrate experimentally the preservation of quantum states in a two-qubit system based on a super-Zeno effect using liquid-state nuclear magnetic resonance techniques. Using inverting radiofrequency pulses and delicately selecting time intervals between two pulses, we suppress the effect of decoherence of quantum states. We observe that preservation of the quantum state ｜11〉 with the super-Zeno effect is three times more efficient than the ordinary one with the standard Zeno effect.
文摘The Zeno time has been calculated for a metastable two-level atom tunneling through a interacting thermal magnetic field. The process of weak measurement has been utilized for the estimation of the timescale. Zeno time has been shown to be temperature dependent. From the calculation it is evident that the Zeno time decreases with the increase of temperature. Moreover, the result restricts the Zeno time to a maximum limiting value, irrespective of how frequent the measurement process is.
基金supported by the National Key Research and Development Program of China(Grant No.2017YFA0303304)the National Natural Science Foundation of China(Grant No.11675016)
文摘The measurement-result-conditioned evolution of a system(e.g., an atom) with spontaneous emissions of photons is described by the quantum trajectory(QT) theory. In this work we generalize the associated QT theory from an infinitely wide bandwidth Markovian environment to the finite bandwidth non-Markovian environment. In particular, we generalize the treatment for an arbitrary spectrum, which is not restricted by the specific Lorentzian case. We rigorously prove the general existence of a perfect scaling behavior jointly defined by the bandwidth of the environment and the time interval between successive photon detections.For a couple of examples, we obtain analytic results to facilitate the QT simulations based on the Monte-Carlo algorithm. For the case where the analytical result is not available, a numerical scheme is proposed for practical simulations.
文摘In the context of continuous piecewise affine dynamical systems and affine complementarity systems with inputs, we study the existence of Zeno behavior, i.e., infinite number of mode transitions in a finite-length time interval, in this paper. The main result reveals that continuous piecewise affine dynamical systems with piecewise real-analytic inputs do not exhibit Zeno behavior. Applied the achieved result to affine complementarity systems with inputs, we also obtained a similar conclusion. A direct benefit of the main result is that one can apply smooth ordinary differential equations theory in a local manner for the analysis of continuous piecewise affine dynamical systems with inputs.
文摘After a brief reference to the quantum Zeno effect, a quantum Zeno paradox is formulated. Our starting point is the usual version of Time Dependent Perturbation Theory. Although this theory is supposed to account for transitions between stationary states, we are led to conclude that such transitions cannot occur. Paraphrasing Zeno, they are nothing but illusions. Two solutions to the paradox are introduced. The first as a straightforward application of the postulates of Orthodox Quantum Mechanics;the other is derived from a Spontaneous Projection Approach to quantum mechanics previously formulated. Similarities and differences between both solutions are highlighted. A comparison between the two versions of quantum mechanics, supporting their corresponding solutions to the paradox, shines a new light on quantum weirdness. It is shown, in particular, that the solution obtained in the framework of Orthodox Quantum Mechanics is defective.
基金supported by the National Natural Science Foundation of China(Grant No.11774047)
文摘We propose a new mechanism, parallel quantum Zeno dynamics, to dissipatively prepare all Bell entangled states of the twoqubit system in the context of cavity quantum electrodynamics. This mechanism can provide two transition channels between ground states and two different dark states simultaneously, which efficiently speeds up the stabilization of the entanglement and suppresses the adverse influence of surrounding environments. In addition, there is no need for the initialization of quantum states and the Clauser-Horne-Shimony-Holt inequality can be violated in a finite temperature bath. The experimental feasibility is also studied by the state-of-the-art technique and a high fidelity about 99% can be achieved.
基金supported by the National Natural Science Foundation of China (Grant Nos. 11704029, and 12174024)supported by the National Natural Science Foundation of China (Grant No. 11504038)。
文摘The study of the polaron of an open quantum system plays an important role in verifying the effectiveness of an approximate many-body theory and predicting novel quantum phenomena in open quantum systems. In a pioneering work, Piazza et al.(2021) proposed a Fermi-polaron scheme with a lossy impurity, which exhibits a novel long-lived attractive polaron branch in the quantum Zeno limit. However, we have encountered a counterpart problem in which an impurity interacting with an open quantum bath scatters exciting polarons, which is what we focus on. In this work, we determine through analytical research the molecular state under the two limits of vanishingly small and infinitely large dissipation intensities as well as the reason why the dissipation range leads to a decrease in the gap between the molecular state and the molecule-hole continuum in the former case.The spectrum functions of molecular and polaron states with different dissipation ranges and loss rates are investigated. We find the spectral signals of molecular and polaron states will first diffuse and then revive as the dissipation increases. Moreover, we show that the attractive and repulsive polarons respond differently to an increasing dissipation range in our model. Finally, we exhibit the polaron energy, residue, effective mass, and two-body decay for mass-balanced and imbalanced systems. Our results might be useful for cold-atom experiments on open quantum systems.
文摘Recently we proposed “a new interpretation of quantum mechanics (called quantum and classical measurement theory)” in this journal (JQIS: Vol. 1, No. 2), which was characterized as the metaphysical and linguistic turn of quantum mechanics. This turn from physics to language does not only realize the remarkable extension of quantum mechanics but also yield the quantum mechanical world view (i.e., the philosophy of quantum mechanics). And thus, the turn urges us to dream that traditional philosophies (i.e., Parmenides, Plato, Aristotle, Descartes, John Locke, Berkeley, Hume, Kant, Saussure, Wittgenstein, etc.) can be understood in the quantum mechanical world view. This dream will be challenged in this paper. We, of course, know that most scientists are skeptical to philosophy. Still, we can expect that readers find a good linguistic philosophy (i.e. philosophy of language) in quantum mechanics.
基金supported by the National Natural Science Foundation of China under Grant No.11405031 and No.11875108the National Natural Science Foundation of Fujian Province China under Grant No.2019J01219。
文摘We propose a scheme to achieve nuclear–nuclear indirect interactions mediated by a mechanically driven nitrogen-vacancy(NV)center in a diamond.Here we demonstrate twoqubit entangling gates and quantum-state transfer between two carbon nuclei.When the dipole–dipole interaction strength is much larger than the driving field strength,the scheme is robust against decoherence caused by coupling between the NV center(nuclear spins)and the environment.Conveniently,precise control of dipole coupling is not required so this scheme is insensitive to fluctuating positions of the nuclear spins and the NV center.Our scheme provides a general blueprint for multi-nuclear-spin gates and for multi-party communication.
基金Supported by the National Fundamental Research Program under Grant No. 2012CB921601National Natural Science Foundation of China under Grant No. 10974028+1 种基金the Doctoral Foundation of the Ministry of Education of China under Grant No. 20093514110009the Natural Science Foundation of Fujian Province under Grant No. 2009J06002
文摘Based on the quantum Zeno dynamics,we propose a two-qubit non-geometric conditional phase gate between two nitrogen-vacancy centers coupled to a whispering-gallery mode cavity.The varying phases design of periodic laser can be used for realizing non-geometric conditional phase gate,and the cavity mode is virtually excited during the gate operation.Thus,the fidelity of the gate operation is insensitive to cavity decay and the fluctuation of the preset laser intensity.The numerical simulation with a realistic set of experimental parameters shows that the gate fidelity 0.987 can be within reached in the near future.
文摘Our main aim is to prove a more general version of the quantum Zeno effect. Then we discuss some examples of the quantum Zeno effect. Furthermore, we discuss a possibility that based on the quantum Zeno effect and certain experiments one could check whether, from the statistical point of view, a concrete system behaves like a quantum system. The more general version of quantum Zeno effect can be helpful to prove that the brain acts like in a quantum system. The proof of our main result is based on certain formulas describing probability distributions of time series related to quantum measurements.
