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
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
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
Quantum Zeno effect with mixed initial state is studied here. Frequent projective measurements performed on a bipartite joint pure state system will result in the quantum Zeno effect on the subsystem of interest. This...Quantum Zeno effect with mixed initial state is studied here. Frequent projective measurements performed on a bipartite joint pure state system will result in the quantum Zeno effect on the subsystem of interest. This shows the existence of Quantum Zeno effect in the system with mixed initial states.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
We experimentally demonstrate the quantum anti-Zeno effect in a two-level system based on a single trapped ion ^（40）Ca~＋. In the large detuning regime, we show that the transfer from the ground state to the excited...We experimentally demonstrate the quantum anti-Zeno effect in a two-level system based on a single trapped ion ^（40）Ca~＋. In the large detuning regime, we show that the transfer from the ground state to the excited state can be remarkably enhanced by the inserted projection measurements. The inserted measurements in our experiment are realized by the electron shelving technique. Compared to the ideal projection measurement, which makes the quantum state collapse instantaneously, a practical electron shelving process needs a finite time duration. The minimum time for this collapse process is shown to be inversely proportional to the square of the coupling strength between the measurement laser and the system.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
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
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 counting. Vertically it is continuous, horizontally it is discrete. While Frege, Tarski, Cantor, Gödel and the Vienna Circle tried to derive the higher dimension from the lower, a procedure that always leads to new contradictions and antinomies (Tarski, Russell), I take the opposite approach here, in which I derive the lower dimension from the higher. This perspective seems to fail because Tarski, Russell, Wittgenstein, and especially the Vienna Circle have shown that the completeness of the absolute itself is logically contradictory. For this reason, we agree with Hegel in assuming that we can never fully comprehend the Absolute, but only its particular manifestations—otherwise we would be putting ourselves in the place of the Absolute, or even God. Nevertheless, we can understand the Absolute in its particular expressions, as I will show with the modest example of the triangle proof of the combined horizontal and vertical countability of the real numbers, which I developed in rejection of Cantor’s diagonal proof. .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
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 (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.
基金Supported by National Natural Science Foundation of China under Grant Nos. 10704001, 61073048, and 11005029the Key Project of Chinese Ministry of Education under Grant No. 210092+2 种基金the Key Program of the Education Department of Anhui Province under Grant Nos. KJ2008A28ZC, 2010SQRL153ZD, and KJ2010A287the "211" Project of Anhui University, the Personnel Department of Anhui ProvinceAnhui Key Laboratory of Information Materials and Devices Anhui University
文摘Quantum Zeno effect with mixed initial state is studied here. Frequent projective measurements performed on a bipartite joint pure state system will result in the quantum Zeno effect on the subsystem of interest. This shows the existence of Quantum Zeno effect in the system with mixed initial states.
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.
基金Project supported by the National Basic Research Program of China(Grant No.2016YFA0301903)the National Natural Science Foundation of China(Grant Nos.11174370,11304387,61632021,11305262,11574398,and N 61205108)the Research Plan Project of National University of Defense Technology,China(Grant No.ZK16-03-04)
文摘We experimentally demonstrate the quantum anti-Zeno effect in a two-level system based on a single trapped ion ^（40）Ca~＋. In the large detuning regime, we show that the transfer from the ground state to the excited state can be remarkably enhanced by the inserted projection measurements. The inserted measurements in our experiment are realized by the electron shelving technique. Compared to the ideal projection measurement, which makes the quantum state collapse instantaneously, a practical electron shelving process needs a finite time duration. The minimum time for this collapse process is shown to be inversely proportional to the square of the coupling strength between the measurement laser and the system.
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.
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.
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 counting. Vertically it is continuous, horizontally it is discrete. While Frege, Tarski, Cantor, Gödel and the Vienna Circle tried to derive the higher dimension from the lower, a procedure that always leads to new contradictions and antinomies (Tarski, Russell), I take the opposite approach here, in which I derive the lower dimension from the higher. This perspective seems to fail because Tarski, Russell, Wittgenstein, and especially the Vienna Circle have shown that the completeness of the absolute itself is logically contradictory. For this reason, we agree with Hegel in assuming that we can never fully comprehend the Absolute, but only its particular manifestations—otherwise we would be putting ourselves in the place of the Absolute, or even God. Nevertheless, we can understand the Absolute in its particular expressions, as I will show with the modest example of the triangle proof of the combined horizontal and vertical countability of the real numbers, which I developed in rejection of Cantor’s diagonal proof. .
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.
