Quantum Zeno effect

“A generalized quantum theoretical framework, not restricted to the validity domain of standard quantum physics, is used to model the dynamics of the bistable perception of ambiguous visual stimuli such as the necker cube. the central idea is to treat the perception process in terms of the evolution of an unstable two-state system. this gives rise to a ‘necker-zeno’ effect, in analogy to the quantum zeno effect. a quantitative relation between the involved time scales is theoretically derived. this relation is found to be satisfied by empirically obtained cognitive time scales relevant for bistable perception.”

“The concept of temporal nonlocality is used to refer to states of a (classical) system that are not sharply localized in time but extend over a time interval of non-zero duration. we investigate the question whether, and how, such a temporal nonlocality can be tested in mental processes. for this purpose we exploit the empirically supported necker-zeno model for bistable perception, which uses formal elements of quantum theory but does not refer to anything like quantum physics of the brain. we derive so-called temporal bell inequalities and demonstrate how they can be violated in this model. we propose an experimental realization of such a violation and discuss some of its consequences for our understanding of mental processes. © 2009 elsevier inc.”

“If frequent measurements ascertain whether a quantum system is still in its initial state, transitions to other states are hindered and the quantum zeno effect takes place. however, in its broader formulation, the quantum zeno effect does not necessarily freeze everything. on the contrary, for frequent projections onto a multidimensional subspace, the system can evolve away from its initial state, although it remains in the subspace defined by the measurement. the continuing time evolution within the projected ‘quantum zeno subspace’ is called ‘quantum zeno dynamics:’ for instance, if the measurements ascertain whether a quantum particle is in a given spatial region, the evolution is unitary and the generator of the zeno dynamics is the hamiltonian with hard-wall (dirichlet) boundary conditions. we discuss the physical and mathematical aspects of this evolution, highlighting the open mathematical problems. we then analyze some alternative strategies to obtain a zeno dynamics and show that they are physically equivalent.”

“The quantum zeno effect is recast in terms of an adiabatic theorem when the measurement is described as the dynamical coupling to another quantum system that plays the role of apparatus. a few significant examples are proposed and their practical relevance discussed. we also focus on decoherence-free subspaces.”

“It is generally impossible to probe a quantum system without disturbing it. however, it is possible to exploit the back-action of quantum measurements and strong couplings to tailor and protect the coherent evolution of a quantum system. this is a profound and counterintuitive phenomenon known as quantum zeno dynamics (qzd). here we demonstrate qzd with a rubidium bose-einstein condensate in a five-level hilbert space. we harness measurements and strong couplings to dynamically disconnect different groups of quantum states and constrain the atoms to coherently evolve inside a two-level subregion. in parallel to the foundational importance due to the realization of a dynamical superselection rule and the theory of quantum measurements, this is an important step forward in protecting and controlling quantum dynamics and, broadly speaking, quantum information processing.”

“A quantum zeno dynamics can be obtained by means of frequent measurements, frequent unitary kicks or a strong continuous coupling and yields a partition of the total hilbert space into quantum zeno subspaces, among which any transition is hindered. we focus on the ‘continuous’ version of the quantum zeno effect and look at several interesting examples. we first analyze these examples in practical terms, towards applications, then propose a novel experiment.”

“The temporal evolution of an unstable quantum mechanical system undergoing repeated measurements is investigated. in general, by changing the time interval between successive measurements, the decay can be accelerated (inverse quantum zeno effect) or slowed down (quantum zeno effect), depending on the features of the interaction hamiltonian. a geometric criterion is proposed for a transition to occur between these two regimes.”

“It was predicted that frequently repeated measurements on an unstable quantum state may alter the decay rate of the state. this is called the quantum zeno effect (qze) or the anti-zeno effect (aze), depending on whether the decay is suppressed or enhanced. in conventional theories of the qze and aze, effects of measurements are simply described by the projection postulate, assuming that each measurement is an instantaneous and ideal one. however, real measurements are not instantaneous and ideal. for the qze and aze by such general measurements, interesting and surprising features have recently been revealed, which we review in this article. the results are based on the quantum measurement theory, which is also reviewed briefly. as a typical model, we consider a continuous measurement of the decay of an excited atom by a photodetector that detects a photon emitted from the atom upon decay. this measurement is an indirect negative-result one, for which the curiosity of the qze and aze is emphasized. it is shown that the form factor is renormalized as a backaction of the measurement, through which the decay dynamics is modified. in a special case of the flat response, where the detector responds to every photon mode with an identical response time, results of the conventional theories are reproduced qualitatively. however, drastic differences emerge in general cases where the detector responds only to limited photon modes. for example, against predictions of the conventional theories, the qze or aze may take place even for states that exactly follow the exponential decay law. we also discuss relation to the cavity quantum electrodynamics. © 2005 elsevier b.v. all rights reserved.”

“We show that the quantum zeno effect can be used to suppress the failure events that would otherwise occur in a linear optics approach to quantum computing. from a practical viewpoint, that would allow the implementation of deterministic logic gates without the need for ancilla photons or high-efficiency detectors. we also show that the photons can behave as if they were fermions instead of bosons in the presence of a strong zeno effect, which leads to an alternative paradigm for quantum computation.”

“We study the exact entanglement dynamics of two atoms in a lossy resonator. besides discussing the steady-state entanglement, we show that in the strong coupling regime the system-reservoir correlations induce entanglement revivals and oscillations and propose a strategy to fight against the deterioration of the entanglement using the quantum zeno effect.”

“Continuous and pulsed quantum zeno effects were observed using a 87rb bose-einstein condensate. oscillations between two ground hyperfine states of a magnetically trapped condensate, externally driven at a transition rate omega(r), were suppressed by destructively measuring the population in one of the states with resonant light. the suppression of the transition rate in the two-level system was quantified for pulsed measurements with a time interval deltat between pulses and continuous measurements with a scattering rate gamma. we observe that the continuous measurements exhibit the same suppression in the transition rate as the pulsed measurements when gammadeltat=3.60(0.43), in agreement with the predicted value of 4. increasing the measurement rate suppressed the transition rate down to 0.005 omega(r).”

“In a quantum world, a watched arrow never moves. this is the quantum zeno effect (qze). repeatedly asking a quantum system ‘are you still in your initial state?’ blocks its coherent evolution through measurement back-action. quantum zeno dynamics (qzd) leaves more freedom to the system. instead of pinning it to a single state, it sets a border in its evolution space. repeatedly asking the system ‘did you cross the border?’ makes it impenetrable. since the border can be designed at will by choosing the measured observable, qzd allows one to tailor the system’s evolution space. recent proposals, particularly in the cavity quantum electrodynamics (cqed) context, highlight the interest of qzd for quantum state engineering tasks, which are the key to quantumenabled technologies and quantum information processing. we report the observation of qzd in the 51-dimension hilbert space of a large angular momentum j = 25. continuous selective interrogation limits the evolution of this angular momentum to an adjustable multi-dimensional subspace. this confined dynamics leads to the production of non-classical ‘schr’odinger cat” states, quantum superpositions of angular momentums pointing in different directions. these states are promising for sensitive metrology of electric and magnetic fields. this qzd approach could be generalized to other systems, opening novel perspectives for quantum information processing.”

“We have previously shown that the quantum zeno effect can be used to implement quantum logic gates for quantum computing applications, where the zeno effect was produced using a strong two-photon absorbing medium. here we show that the zeno effect can also be used to implement classical logic gates whose inputs and outputs are high-intensity fields (coherent states). the operation of the devices can be understood using a quasistatic analysis, and their switching times are calculated using a dynamic approach. the two-photon absorption coefficient of rubidium vapor is shown to allow operation of these devices at relatively low power levels.”

“We present a theoretical study of a superconducting charge qubit dispersively coupled to a transmission line resonator. starting from a master equation description of this coupled system and using a polaron transformation, we obtain an exact effective master equation for the qubit. we then use quantum trajectory theory to investigate the measurement of the qubit by continuous homodyne measurement of the resonator out-field. using the same porlaron transformation, a stochastic master equation for the conditional state of the qubit is obtained. from this result, various definitions of the measurement time are studied. furthermore, we find that in the limit of strong homodyne measurement, typical quantum trajectories for the qubit exhibit a crossover from diffusive to jump-like behavior. finally, in the presence of rabi drive on the qubit, the qubit dynamics is shown to exhibit quantum zeno behavior.”

“As of october 2006, there were approximately 535 citations to the seminal 1977 paper of misra and sudarshan that pointed out the quantum zeno paradox (more often called the quantum zeno effect). in simple terms, the quantum zeno effect refers to a slowing down of the evolution of a quantum state in the limit that the state is observed continuously. there has been much disagreement as to how the quantum zeno effect should be defined and as to whether it is really a paradox, requiring new physics, or merely a consequence of ‘ordinary’ quantum mechanics. the experiment of itano, heinzen, bollinger, and wineland, published in 1990, has been cited around 347 times and seems to be the one most often called a demonstration of the quantum zeno effect. given that there is disagreement as to what the quantum zeno effect is, there naturally is disagreement as to whether that experiment demonstrated the quantum zeno effect. some differing perspectives regarding the quantum zeno effect and what would constitute an experimental demonstration are discussed.”

“We report the first observation of the quantum zeno and anti-zeno effects in an unstable system. cold sodium atoms are trapped in a far-detuned standing wave of light that is accelerated for a controlled duration. for a large acceleration the atoms can escape the trapping potential via tunneling. initially the number of trapped atoms shows strong nonexponential decay features, evolving into the characteristic exponential decay behavior. we repeatedly measure the number of atoms remaining trapped during the initial period of nonexponential decay. depending on the frequency of measurements we observe a decay that is suppressed or enhanced as compared to the unperturbed system.”

“In theory, the decay of any unstable quantum state can be inhibited by sufficiently frequent measurements–the quantum zeno effect. although this prediction has been tested only for transitions between two coupled, essentially stable states, the quantum zeno effect is thought to be a general feature of quantum mechanics, applicable to radioactive or radiative decay processes. this generality arises from the assumption that, in principle, successive observations can be made at time intervals too short for the system to change appreciably. here we show not only that the quantum zeno effect is fundamentally unattainable in radiative or radioactive decay (because the required measurement rates would cause the system to disintegrate), but also that these processes may be accelerated by frequent measurements. we find that the modification of the decay process is determined by the energy spread incurred by the measurements (as a result of the time-energy uncertainty relation), and the distribution of states to which the decaying state is coupled. whereas the inhibitory quantum zeno effect may be feasible in a limited class of systems, the opposite effect–accelerated decay–appears to be much more ubiquitous.”

“The quantum zeno effect, i.e. the inhibition of coherent quantum dynamics by projective measurements is one of the most intriguing predictions of quantum mechanics. here we experimentally demonstrate the quantum zeno effect by inhibiting the microwave driven coherent spin dynamics between two ground state spin levels of the nitrogen vacancy center in diamond nano-crystals. our experiments are supported by a detailed analysis of the population dynamics via a semi-classical model.”

“We demonstrate that near threshold decay processes may be accelerated by repeated measurements. examples include near threshold photodetachment of an electron from a negative ion, and spontaneous emission in a cavity close to the cutoff frequency, or in a photon band gap material.”

“Misra and sudarshan pointed out, based on the quantum measurement theory, that repeated measurements lead to a slowing down of the transition, which they called the quantum zeno effect. recently, itano, heinzen, bollinger and wineland have reported that they succeeded in observing that effect. we show that the results of itano et al. can be recovered through conventional quantum mechanics and do not involve a repeated reduction of the wave function. © 1990.”

“No one has ever touched zeno without refuting him’’. we will not refute zeno in this paper. instead we review some unexpected encounters of zeno with modern science. the paper begins with a brief biography of zeno of elea followed by his famous paradoxes of motion. reflections on continuity of space and time lead us to banach and tarski and to their celebrated paradox, which is in fact not a paradox at all but a strict mathematical theorem, although very counterintuitive. quantum mechanics brings another flavour in zeno paradoxes. quantum zeno and anti-zeno effects are really paradoxical but now experimental facts. then we discuss supertasks and bifurcated supertasks. the concept of localization leads us to newton and wigner and to interesting phenomenon of quantum revivals. at last we note that the paradoxical idea of timeless universe, defended by zeno and parmenides at ancient times, is still alive in quantum gravity. the list of references that follows is necessarily incomplete but we hope it will assist interested reader to fill in details.”

“Heat flow between a large thermal ‘bath’ and a smaller system brings them progressively closer to thermal equilibrium while increasing their entropy. fluctuations involving a small fraction of a statistical ensemble of systems interacting with the bath result in deviations from this trend. in this respect, quantum and classical thermodynamics are in agreement. here we predict a different trend in a purely quantum mechanical setting: disturbances of thermal equilibrium between two-level systems (tlss) and a bath, caused by frequent, brief quantum non-demolition measurements of the tls energy states. by making the measurements increasingly frequent, we encounter first the anti-zeno regime and then the zeno regime (namely where the tlss’ relaxation respectively speeds up and slows down). the corresponding entropy and temperature of both the system and the bath are then found to either decrease or increase depending only on the rate of observation, contrary to the standard thermodynamical rules that hold for memory-less (markov) baths. from a practical viewpoint, these anomalies may offer the possibility of very fast control of heat and entropy in quantum systems, allowing cooling and state purification over an interval much shorter than the time needed for thermal equilibration or for a feedback control loop.”