Short pulses of a probe laser have been used in the past to measure whether a two-level atom is in its ground or excited state. The probe pulse couples the ground state to a third, auxiliary, level of the atom. Occurrence or absence of resonance fluorescence were taken to mean that the atom was found in its ground or excited state, respectively. In this paper we investigate to what extent this procedure results in an effective measurement to which the projection postulate can be applied, at least approximately. We discuss in detail the complications arising from an additional time development of the two-level system proper during a probe pulse. We extend our previous results for weak probe pulses to the general case and show that one can model an ideal (projection-postulate) measurement much better with a strong than a weak probe pulse. In an application to the quantum Zeno effect we calculate the slow-down of the atomic time development under n repeated probe pulse measurements and determine the corrections compared to the case of n ideal measurements.
The time evolution of an unstable quantum mechanical system coupled with an external measuring agent is investigated. According to the features of the interaction Hamiltonian, a quantum Zeno effect (hindered decay) or an inverse quantum Zeno effect (accelerated decay) can take place, depending on the response time of the apparatus. The transition between the two regimes is analyzed for both pulsed and continuous measurements.
The dynamics of a quantum system undergoing measurements is investigated. Depending on the features of the interaction Hamiltonian, the decay can be slowed (quantum Zeno effect) or accelerated (inverse quantum Zeno effect), by changing the time interval between successive (pulsed) measurements or, alternatively, by varying the "strength" of the (continuous) measurement.
A relation is found between pulsed measurements of the excited state probability of a two-level atom illuminated by a driving laser, and a continuous measurement by a second laser coupling the excited state to a third state which decays rapidly and irreversibly. We find the time between pulses to achieve the same average detection time than a given continuous measurement in strong, weak, or intermediate coupling regimes, generalizing the results in L. S. Schulman, Phys. Rev. A 57, 1509 (1998).
We construct an algorithm for suppressing the transitions of a quantum mechanical system, initially prepared in a subspace P of the full Hilbert space of the system, to outside this subspace by subjecting it to a sequence of unequally spaced short-duration pulses. Each pulse multiplies the amplitude of the vectors in the subspace by -1. The number of pulses required by the algorithm to limit the leakage probability to $ε$ in time $T$ increases as $T \exp[ \sqrt{\log(T^2/ε)}]$, compared to $T^2 ε^{-1}$ in the standard quantum Zeno effect.
We analyse non-quadratic in time Zeno effect which arises when a few-atom state initially trapped between two high laser-induced barriers is briefly released to free evolution. We identify the Zeno time, analyse the energy distributions of those atoms which have escaped an remained inside the trap, and obtain a simple relation between the survival and non-escape probabilities. The relevant time scales are such that the effect would be observable for the atomic species used in current laser experiments.
We unify the quantum Zeno effect (QZE) and the "bang-bang" (BB) decoupling method for suppressing decoherence in open quantum systems: in both cases strong coupling to an external system or apparatus induces a dynamical superselection rule that partitions the open system's Hilbert space into quantum Zeno subspaces. Our unification makes use of von Neumann's ergodic theorem and avoids making any of the symmetry assumptions usually made in discussions of BB. Thus we are able to generalize BB to arbitrary fast and strong pulse sequences, requiring no symmetry, and to show the existence of two alt…
The quantum Zeno effect (QZE) predicts a slow-down of the time development of a system under rapidly repeated ideal measurements, and experimentally this was tested for an ensemble of atoms using short laser pulses for non-selective state measurements. Here we consider such pulses for selective measurements on a single system. Each probe pulse will cause a burst of fluorescence or no fluorescence. If the probe pulses were strictly ideal measurements, the QZE would predict periods of fluorescence bursts alternating with periods of no fluorescence (light and dark periods) which would become long…
We point out that the quantum Zeno effect, i.e., inhibition of spontaneous decay by frequent measurements, is observable only in spectrally finite reservoirs, i.e., in cavities and waveguides, using a sequence of evolution-interrupting pulses or randomly-modulated CW fields. By contrast, such measurements can only accelerate decay in free space.
We present a proposal to realize the quantum Zeno effect (QZE) and quantum Zeno-like effect (QZLE) in a proximal $\mathrm{^{13}C}$ nuclear spin by controlling a proximal electron spin of a nitrogen vacancy (NV) center. The measurement is performed by applying a microwave pulse to induce the transition between different electronic spin states. Under the practical experimental conditions, our calculations show that there exist both QZE and QZLE in a $^{13}$C nuclear spin in the vicinity of an NV center.
We have previously shown that two-photon absorption (TPA) and the quantum Zeno effect can be used to make deterministic quantum logic devices from an otherwise linear optical system. Here we show that this type of quantum Zeno gate can be used with additional two-photon absorbing media and weak laser pulses to make a heralded single photon source. A source of this kind is expected to have a number of practical advantages that make it well suited for large scale quantum information processing applications.
Quantum Zeno effect is a significant tool in quantum manipulating and computing. We propose its observation in superconducting phase qubit with two experimentally feasible measurement schemes. The conventional measurement method is used to achieve the proposed pulse and continuous readout of the qubit state, which are analyzed by projection assumption and Monte Carlo wave-function simulation, respectively. Our scheme gives a direct implementation of quantum Zeno effect in a superconducting phase qubit.
Repeated measurements of a quantum particle to check its presence in a region of space was proposed long ago [G. R. Allcock, Ann. Phys. {\bf 53}, 286 (1969)] as a natural way to determine the distribution of times of arrival at the orthogonal subspace, but the method was discarded because of the quantum Zeno effect: in the limit of very frequent measurements the wave function is reflected and remains in the original subspace. We show that by normalizing the small bits of arriving (removed) norm, an ideal time distribution emerges in correspondence with a classical local-kinetic-energy distribu…
Decoherence time has been calculated for an optical ion trap of Be atoms in a bistable potential model. Comparison has been made between decoherence time and Zeno time for double well potential as a special case. Zeno time is considered as a lower limit of decoherence time for sustainable quantum coherence. Equality of the respective timescales provides a certain transitional temperature, below which decoherence can be asymptotically minimized.
Using numerical calculations, we compare the collective transition probabilities of many spins in random magnetic fields, subject to either frequent projective measurements, frequent phase modulations, or a mix of modulations and measurements. For three different distribution functions (Gaussian, Lorentzian, and exponential) we consider here, the transition probability under frequent modulations is suppressed most if the pulse delay is short and the evolution time is larger than a critical value. Furthermore, decoherence freezing (with a transition rate equals to zero) occurs when there are fr…
The projection postulate has been used to predict a slow-down of the time evolution of the state of a system under rapidly repeated measurements, and ultimately a freezing of the state. To test this so-called quantum Zeno effect an experiment was performed by Itano et al. (Phys. Rev. A 41, 2295 (1990)) in which an atomic-level measurement was realized by means of a short laser pulse. The relevance of the results has given rise to controversies in the literature. In particular the projection postulate and its applicability in this experiment have been cast into doubt. In this paper we show anal…
The quantum Zeno effect is well-known for fixing a system to an eigenstate by frequent measurements. It is also known that applying frequent unitary pulses induces a Zeno subspace that can also pin the system to an eigenspace. Both approaches have been studied as means to maintain a system in a certain subspace. Extending the two concepts, we consider making the measurements/pulses dynamical so that the state can move with the motion of the measurement axis/pulse basis. We show that the system stays in the dynamical eigenbasis when the measurements/pulses are slowly changing. Explicit bounds f…
A general coherent control scenario to suppress, or accelerate, tunneling of quantum states decaying into a continuum, is investigated. The method is based on deterministic, or stochastic, sequences of unitary pulses that affect the underlying interference phenomena responsible for quantum dynamics, without inducing decoherence, or collapsing the coherent evolution of the system. The influence of control sequences on the ensuing quantum dynamics is analyzed by using perturbation theory to first order in the control pulse fields and compared to dynamical decoupling (DD) protocols and sequences …
We investigate the effect of nuclear spins on the phase shift and polarisation rotation of photons scattered off a quantum dot-cavity system. We show that as the phase shift depends strongly on the resonance energy of an electronic transition in the quantum dot, it can provide a sensitive probe of the quantum state of nuclear spins that broaden this transition energy. By including the electron-nuclear spin coupling at a Hamiltonian level within an extended input-output formalism, we show how a photon scattering event acts as a nuclear spin measurement, which when rapidly applied leads to an in…
An efficient coding circuit is given for the perfect quantum error correction of a single qubit against arbitrary 1-qubit errors within a 5 qubit code. The circuit presented employs a double `classical' code, i.e., one for bit flips and one for phase shifts. An implementation of this coding circuit on an ion-trap quantum computer is described that requires 26 laser pulses. A further circuit is presented requiring only 24 laser pulses, making it an efficient protection scheme against arbitrary 1-qubit errors. In addition, the performance of two error correction schemes, one based on the quantum…
We demonstrate through exact solutions that a spin bath leads to stronger (faster) dephasing of a qubit than a bosonic bath with identical bath-coupling spectrum. This difference is due to the spin-bath "dressing" by the coupling. Consequently, the quantum statistics of the bath strongly affects the pulse sequences required to dynamically decouple the qubit from its bath.
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 d…
The driven evolution of the spin of an individual atomic ion on the ground-state hyperfine resonance is impeded by the observation of the ion in one of the pertaining eigenstates. Detection of resonantly scattered light identifies the ion in its upper ``bright'' state. The lower ``dark'' ion state is free of relaxation and correlated with the detector by a null signal. Null events represent the straightforward demonstration of the quantum Zeno paradox. Also, high probability of survival was demonstrated when the ion, driven by a fractionated $π$ pulse, was probed {\em and monitored} during the…
The so-called quantum Zeno effect is essentially a consequence of the projection postulate for ideal measurements. To test the effect Itano et al. have performed an experiment on an ensemble of atoms where rapidly repeated level measurements were realized by means of short laser pulses. Using dynamical considerations we give an explanation why the projection postulate can be applied in good approximation to such measurements. Corrections to ideal measurements are determined explicitly. This is used to discuss in how far the experiment of Itano et al. can be considered as a test of the quantum …
The dynamics of any quantum system is unavoidably influenced by the external environment. Thus, the observation of a quantum system (probe) can allow the measure of the environmental features. Here, to spectrally resolve a noise field coupled to the quantum probe, we employ dissipative manipulations of the probe, leading to so-called Stochastic Quantum Zeno (SQZ) phenomena. A quantum system coupled to a stochastic noise field and subject to a sequence of protective Zeno measurements slowly decays from its initial state with a survival probability that depends both on the measurement frequency …
We discuss a proposal for the efficient generation of the maximally entangled atomic N-GHZ state in a spinor-1 condensate by driving internal state atomic Raman transitions using (classical) laser fields. We illustrate the dynamics in terms of a quantum Zeno subspace, and identify the resultant atomic elastic collision in facilitating the deterministic entanglement creation. Our proposal can be readily implemented in several laboratories where ferromagnetic spinor condensates (of $^{87}$Rb atoms) are investigated.
A new systematic strategy for steering the distillation process for a quantum system, that utilizes the so-called "pulsed" and "continuous" measurements on another quantum system in interaction with the former, is proposed. The distillation process characterized by the specific interaction between the two systems and the "pulsed" measurements is shown to be controllable through the "continuous" measurements, i.e., the quantum Zeno dynamics, providing an effective recipe to prefix the target.
We propose a scheme for a two-qubit conditional phase gate by quantum Zeno effect with semiconductor quantum dots. The system consists of two charged dots and one ancillary dot that can perform Rabi oscillations under a resonant laser pulse. The quantum Zeno effect is induced by phonon-assisted exciton relaxation between the ancillary dot and the charged dots, which is equivalent to a continuous measurement. We solve analytically the master equation and simulate the dynamics of the system using a realistic set of parameters. In contrast to standard schemes, larger phonon relaxation rates incre…
Quantum mechanics predicts that our physical reality is influenced by events that can potentially happen but factually do not occur. Interaction-free measurements (IFMs) exploit this counterintuitive influence to detect the presence of an object without requiring any interaction with it. Here we propose and realize an IFM concept based on an unstable many-particle system. In our experiments, we employ an ultracold gas in an unstable spin configuration which can undergo a rapid decay. The object - realized by a laser beam - prevents this decay due to the indirect quantum Zeno effect and thus, i…
This paper shows that under certain symmetry conditions the probability of remaining in the initial state (the probability of no transition) in a chainwise-connected multistate system driven by two or more delayed laser pulses does not depend on the pulse order.
Frequent Measurements on an unstable particle located at observable initial state freeze the particle on this state, known as quantum Zeno effect [1-14]. Measurements on an observable subspace further open the prelude of quantum Zeno dynamics [15-17]. These phenomena affect the results of quantum measurement that has been widely used in quantum information and quantum computation [18-21]. However, this common argument is insufficient when the initial state is coupled with a continuum reservoir. In such an irreversible system, intrinsic decay property destroys the frozen behavior. Although it h…
We study the state decay of two qubits interacted with a common harmonic oscillator reservoir. There are both decoherence error and the error caused by the amplitude change of the superradiant state. We show that frequent $π$-phase pulses can eliminate both typpes of errors therefore protect a two-qubit odd-parity state more effectively than the frequent measurement method. This shows that the the methods using dynamical decoupling and the quantum Zeno effects actually can give rather {\em different} results when the operation frequency is finite.
In this paper the Klein-Gordon equation (K-GE) is solved for the interaction of attosecond laser pulses with medium in which Casimir force operates. It is shown that for nanoscale structures, NEMS and MEMS, the attosecond laser pulses can be used as the tool for the investigation of the role played by Casimir force on the nanoscale. Key words: Casimir force; NEMS, MEMS, Attosecond laser pulses.
We consider the evolution of an arbitrary quantum dynamical semigroup of a finite-dimensional quantum system under frequent kicks, where each kick is a generic quantum operation. We develop a generalization of the Baker-Campbell-Hausdorff formula allowing to reformulate such pulsed dynamics as a continuous one. This reveals an adiabatic evolution. We obtain a general type of quantum Zeno dynamics, which unifies all known manifestations in the literature as well as describing new types.
We propose a new laser cooling method for atomic species whose level structure makes traditional laser cooling difficult. For instance, laser cooling of hydrogen requires vacuum-ultraviolet laser light, while multielectron atoms need laser light at many widely separated frequencies. These restrictions can be eased by laser cooling on two-photon transitions with ultrafast pulse trains. Laser cooling of hydrogen, antihydrogen, and carbon appears feasible, and extension of the technique to molecules may be possible.
A model for quantum Zeno effect based upon an effective Schrödinger equation originated by the path-integral approach is developed and applied to a two-level system simultaneously stimulated by a resonant perturbation. It is shown that inhibition of stimulated transitions between the two levels appears as a consequence of the influence of the meter whenever measurements of energy, either continuous or pulsed, are performed at quantum level of sensitivity. The generality of this approach allows to qualitatively understand the inhibition of spontaneous transitions as the decay of unstable partic…
The technological possibilities of a realistic eavesdropper are discussed. Two eavesdropping strategies taking profit of multiphoton pulses in faint laser QKD are presented. We conclude that, as long as storage of Qubits is technically impossible, faint laser QKD is not limited by this security issue, but mostly by the detector noise.
We experimentally demonstrate the freezing of evolution of quantum states in one- and two-dimensional subspaces of two qubits, on an NMR quantum information processor. State evolution was frozen and leakage of the state from its subspace to an orthogonal subspace was successfully prevented using super-Zeno sequences, comprising of a set of inverting radio frequency (rf) pulses punctuated by pre-selected time intervals. We demonstrate the efficacy of the scheme by preserving different types of states, including separable and maximally entangled states in one- and two-dimensional subspaces of tw…
Implementation of quantum logical gates for multilevel system is demonstrated through decoherence control under the quantum adiabatic method using simple phase modulated laser pulses. We make use of selective population inversion and Hamiltonian evolution with time to achieve such goals robustly instead of the standard unitary transformation language.
A tenet of time-resolved spectroscopy is -faster laser pulses for shorter timescales- . Here we suggest turning this paradigm around, and slow down the system dynamics via repeated measurements, to do spectroscopy on longer timescales. This is the principle of the quantum Zeno effect. We exemplify our approach with the Auger process, and find that repeated measurements increase the core-hole lifetime, redistribute the kinetic energy of Auger electrons, and alter entanglement formation. We further provide an explicit experimental protocol for atomic Li, to make our proposal concrete.
We consider inter-atomic forces due to resonant dipole-dipole interactions within a dimer of highly excited Rydberg atoms, embedded in an ultra-cold gas. These forces rely on a coherent superposition of two-atom electronic states, which is destroyed by continuous monitoring of the dimer state through a detection scheme utilizing controllable interactions with the background gas atoms. We show that this intrinsic decoherence of the molecular energy surface can gradually deteriorate a repulsive dimer state, causing a mixing of attractive and repulsive character. For sufficiently strong decoheren…
We report on experiments exploring the non-Hermitian dynamics of pairs of two-level atoms tightly confined in an optical lattice and driven by a near-resonant laser. Although spontaneous emission is negligible for the long-lived excited state, two-body dissipation arises from strong inelastic collisions between two atoms in the excited state. We demonstrate quasi-adiabatic control of the internal state of the pairs in the quantum Zeno regime where inelastic losses dominate. Preparing each atom pair in the longest-lived eigenstate of the non-Hermitian Hamiltonian describing the dissipative dyna…
We show how engineered classical noise can be used to generate constrained Hamiltonian dynamics in atomic quantum simulators of many-body systems, taking advantage of the continuous Zeno effect. After discussing the general theoretical framework, we focus on applications in the context of lattice gauge theories, where imposing exotic, quasi-local constraints is usually challenging. We demonstrate the effectiveness of the scheme for both Abelian and non-Abelian gauge theories, and discuss how engineering dissipative constraints substitutes complicated, non-local interaction patterns by global c…
Quantum-mechanical investigation is presented to study single attosecond pulse generation by gating high-order harmonic emission from H$_2^+$ molecule in intense laser pulses with time-dependent ellipticity. The high-order harmonic generation from H$_2^+$ molecule in superposition of a left and a right-hand circularly polarized Gaussian pulse is studied and the effect of time duration and carrier-envelope phase of laser field on single attosecond pulse generation is investigated. Using laser field formed by combination of a left and a right-hand elliptically polarized Gaussian pulse, the effec…
The recent developments of high intensity ultra-short laser pulses have raised the hopes of observing Schwinger vacuum pair production which is one of the important non-perturbative phenomena in Quantum electrodynamics (QED). The quantitative analysis of realistic high intensity laser pulses is vital for understanding the effect of the field parameters on the momentum spectrum of the produced particles. In this study, we analyze chirped laser pulses with a sub-cycle structure, and investigate the effects of the chirp parameter on the momentum spectrum of the produced particles. The combined ef…
We study theoretically fast transfer of excitons between pairs of coupled quantum dots driven by the optical Stark effect that is produced by a short nonresonant laser pulse. The Schrödinger equation, in which the relative position of energy levels of quantum dot subsystems is time-dependent, is solved numerically. Computer simulation shows a way to achieve efficient excitation transfer by the action of a picosecond laser pulse with a rectangular envelope function.
We prove the existence of uniform limits for certain sequences of products of contractions and elements of a family of uniformly continuous propagators acting on a Hilbert or a Banach space. From the point of view of Quantum Physics, the considered sequences can represent the evolution of a system whose dynamics, described by a continuous propagator, is disturbed by a sequence of generic quantum operations (e.g., projective measurements or unitary pulses). This includes and also generalizes the so-called quantum Zeno dynamics. The time-evolution obtained from the limits of the considered seque…
In recent years it became possible to align molecules in free space using ultrashort laser pulses. Here we explore two schemes for controlling molecule-surface scattering process, which are based on the laser-induced molecular alignment. In the first scheme, a single ultrashort non-resonant laser pulse is applied to a molecular beam hitting the surface. This pulse modifies the angular distribution of the incident molecules, and causes the scattered molecules to rotate with a preferred sense of rotation (clockwise or counter-clockwise). In the second scheme, two properly delayed laser pulses ar…
We propose a mechanism to produce a superposition of atomic and molecular states by a train of ultrashort laser pulses combined with weak control fields. By adjusting the repetition rate of the pump pulses and the intensity of the coupling laser, one can suppress a transition while simultaneously enhancing the desired transitions. As an example, various superpositions of vibrational states of the $K_2$ molecule are shown.
