arXiv subjects

Adam Zaman Chaudhry

Publications and source records attributed to Adam Zaman Chaudhry.

30 records · Page 2Linked to original sources

arXiv2018

The quantum Zeno and anti-Zeno effects with non-selective measurements

In studies of the quantum Zeno and anti-Zeno effects, it is usual to consider rapid projective measurements with equal time intervals being performed on the system to check whether or not the system is in the initial state. These projective measurements are selective measurements in the sense that the measurement results are read out and only the case where all the measurement results correspond to the initial state is considered in the analysis of the effect of the measurements. In this paper, we extend such a treatment to consider the effect of repeated non-selective measurements - only the final measurement is required to correspond to the initial state, while we do not know the results of the intermediate measurements. We present a general formalism to derive the effective decay rate of the initial quantum state with such non-selective measurements. Importantly, we show that there is a difference between using non-selective measurements and the usual approach of considering only selective measurements only if we go beyond the weak system-environment coupling regime in models other than the usual population decay models. As such, we then apply our formalism to investigate the quantum Zeno and anti-Zeno effects for three exactly solvable system-environment models: a single two-level system undergoing dephasing, a single two-level system interacting with an environment of two-level systems, and a large spin undergoing dephasing. Our results show that the quantum Zeno and anti-Zeno effects in the presence of non-selective measurements can differ very significantly as compared to the repeated selective measurement scenario.

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arXiv2018

Effect of initial system-environment correlations with spin environments

Understanding the dynamics of open quantum systems is a highly important task for the implementation of emerging quantum technologies. To make the problem tractable theoretically, it is common to neglect initial system-environment correlations. However, this assumption is questionable in situations where the system is interacting strongly with the environment. In particular, the system state preparation can then influence the dynamics of the system via the system-environment correlations. To gain insight into the effect of these correlations, we solve an exactly solvable model of a quantum spin interacting with a spin environment both with and without initial correlations for arbitrary system-environment coupling strengths. We show that the effect of the system state preparation may or may not be significant in the strong system-environment coupling regime at low temperatures. We also study the dynamics of the entanglement between two spins interacting with a common spin environment with and without initial system-environment correlations to demonstrate that the correlations can play a significant role in the dynamics of two-qubit systems as well.

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arXiv2017

Analyzing the Quantum Zeno and anti-Zeno effects using optimal projective measurements

Measurements in quantum mechanics can not only effectively freeze the state of the quantum system (the quantum Zeno effect) but also accelerate the time evolution of the system (the quantum anti-Zeno effect). In studies of the quantum Zeno and anti-Zeno effects, a quantum state, usually an excited state of the system, is prepared repeatedly by projecting the quantum state onto the initial state again and again. In this paper, we repeatedly prepare the initial quantum state in a different manner. Instead of only performing projective measurements, we allow unitary operations to be performed, on a very short time-scale, after each measurement. We can then repeatedly prepare the initial quantum state by performing some projective measurement and thereafter, after each measurement, performing a suitable unitary operation to repeatedly end up with the initial state. Our objective thereafter is to find the projective measurements that need to repeatedly performed such that we obtain the minimum possible effective decay rate of the quantum state. Consequently, the quantum state is maximally protected from its environment. We find that these optimized projective measurements keep on changing depending on the measurement time interval. We explicitly find the projective measurements that need to be performed, as well as the optimized effective decay rate, for a variety of system-environment models such as the population decay model, the pure dephasing model, the spin-boson model, and the large spin-boson model. We find that there can be considerable differences between this optimized effective decay rate and the usual decay rate obtained by repeatedly projecting onto the initial state. In particular, the Zeno and anti-Zeno regimes can be considerably modified.

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arXiv2017

The quantum Zeno and anti-Zeno effects with strong system-environment coupling

The fact that repeated projective measurements can slow down (the Zeno effect) or speed up (the anti-Zeno effect) quantum evolution is well-known. However, to date, studies of these effects focus on quantum systems that are weakly interacting with their environment. In this paper, we investigate what happens to a quantum system under the action of repeated measurements if the quantum system is strongly interacting with its environment. We consider as the quantum system a single two-level system coupled strongly to a collection of harmonic oscillators. A so-called polaron transformation is then used to make the problem in the strong system-environment coupling regime tractable. We find that the strong coupling case exhibits quantitative and qualitative differences as compared with the weak coupling case. In particular, the effective decay rate does not depend linearly on the spectral density of the environment. This then means that, in the strong coupling regime that we investigate, increasing the system-environment coupling strength can actually decrease the effective decay rate. We also consider a collection of two-level atoms coupled strongly with a common environment. In this case, we find that there are further differences between the weak and strong coupling cases since the two-level atoms can now indirectly interact with one another due to the common environment.

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arXiv2016

A general framework for the Quantum Zeno and anti-Zeno effects

A general treatment of the quantum Zeno and anti-Zeno effects is presented which is valid for an arbitrary system-environment model in the weak system-environment coupling regime. It is shown that the effective lifetime of a quantum state that is subjected to repeated projective measurements depends on the overlap of the spectral density of the environment and a generalized `filter function' which in turn depends on the system state that is repeatedly being prepared, the measurement interval, the system parameters, the system-environment coupling, and the environment correlation function. This general framework is then used to study explicitly the Zeno to anti-Zeno crossover behavior for the spin-boson model where a single two-level system is coupled to a bosonic environment. It is shown that our framework reproduces results for the usual population decay case as well as for the pure dephasing model, while at the same time allowing us to study the Zeno to anti-Zeno transition when both decay and dephasing take place. These results are then extended to many two-level systems coupled collectively to the bosonic environment to show that the distinction between the Zeno and anti-Zeno effects becomes more pronounced as the number of two-level systems increases.

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arXiv2014

Detecting magnetic fields using Nitrogen-Vacancy Centers

We show how nitrogen-vacancy centers can be used to `detect' magnetic fields, that is, to find out whether a magnetic field, about which we may not have complete information, is actually present or not. The solution to this problem comes from quantum state discrimination theory. The effect of decoherence is taken into account to optimize the time over which the nitrogen-vacancy center is allowed to interact with the magnetic field before making a measurement. We also find the optimum measurement that should be performed. We then show how multiple measurements reduce the error in detecting the magnetic field. Finally, a major limitation of the measurement process, namely limited photon detection efficiency, is taken into account. Our proposals should be implementable with current experimental technology.

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arXiv2014

Utilizing Nitrogen Vacancy Centers to measure oscillating magnetic fields

We show how nitrogen vacancy (NV) centers can be used to determine the amplitude, phase and frequency of unknown weak monochromatic and multichromatic oscillating magnetic fields using only the periodic dynamical decoupling (PDD) and Carr-Purcell-Meiboom-Gill (CPMG) sequences. The effect of decoherence on the measurement of the magnetic field parameters is explicitly analyzed, and we take into account the fact that different pulse sequences suppress decoherence to different extents. Since the sensitivity increases with increasing sensing time while it decreases due to decoherence, we use the Fisher information matrix in order to optimize the number of pulses that should be used.

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arXiv2014

Zeno and anti-Zeno effects on Dephasing

Quantum Zeno and anti-Zeno effects on pure dephasing are studied using exactly solvable microscopic models. The crossover between these two opposite effects is investigated. The case of a single two-level system undergoing dephasing is already different from the previously studied population decay problem, even without taking into account any back action from the environment. For many two-level systems interacting with a common environment, multiple transitions between Zeno and anti-Zeno regimes are predicted. Finally, if the system-environment coupling strength is not weak, we show that the nontrivial evolution of the environment between measurements can considerably alter the quantum Zeno and anti-Zeno effects.

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arXiv2013

Role of initial system-environment correlations: A master equation approach

In order to achieve practical implementations of emerging quantum technologies, it is important to have a firm understanding of the dynamics of realistic quantum open systems. Master equations provide a widely used tool in this regard. In this work, we first construct a master equation, valid for weak system-environment coupling, which explicitly takes into account the impact of preparing an initial system state from an equilibrium system-environment state that has system-environment correlations. We then investigate the role of initial system-environment correlations using this master equation for a system consisting of many two-level atoms interacting with a common environment. We show that, in general, due to the initial system-environment correlations before a state preparation, the quantum state of the system can evolve at a faster time-scale. Moreover, we also consider different initial state preparations, and demonstrate that the influence of state preparations depends on the initial states prepared. Our results can be of interest to many topics based on quantum open systems where system-environment correlation effects have been neglected before.

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arXiv2012

Amplification and suppression of system-bath correlation effects in an open many-body system

Understanding the rich dynamics of open quantum systems is of fundamental interest to quantum control and quantum information processing. By considering an open system of many identical two-level atoms interacting with a common bath, we show that effects of system-bath correlations are amplified in a many-body system via the generation of a short time scale inversely proportional to the number of atoms. Effects of system-bath correlations are therefore considerable even when each individual atom interacts with the bath weakly. We further show that correlation-induced dynamical effects may still be suppressed via the dynamical decoupling approach, but they present a challenge for quantum state protection as the number of atom increases.

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arXiv2012

Protecting and Enhancing Spin Squeezing via Continuous Dynamical Decoupling

Realizing useful quantum operations with high fidelity is a two-task quantum control problem wherein decoherence is to be suppressed and desired unitary evolution is to be executed. The dynamical decoupling (DD) approach to decoherence suppression has been fruitful but synthesizing DD fields with certain quantum control fields may be experimentally demanding. In the context of spin squeezing, here we explore an unforeseen possibility that continuous DD fields may serve dual purposes at once. In particular, it is shown that a rather simple configuration of DD fields can suppress collective decoherence and yield a 1/N scaling of the squeezing performance (N is the number of spins), thus making spin squeezing more robust to noise and much closer to the so-called Heisenberg limit. The theoretical predictions should be within the reach of current spin squeezing experiments.

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arXiv2011

Decoherence control: Universal protection of two-qubit states and two-qubit gates using continuous driving fields

A field configuration utilizing local static and oscillating fields is constructed to achieve universal (but low-order) protection of two-qubit states. That is, two-qubit states can be protected against arbitrary system-environment coupling if the driving field frequency, as compared with the cutoff frequency of the environment, is sufficiently large. Equally important, we show that it is possible to construct driving fields to protect two-qubit entangling gates against decoherence, without assuming any particular form of system-environment coupling. Using a non-Markovian master equation, we further demonstrate the effectiveness of our continuous dynamical decoupling fields in protecting entanglement and the excellent performance of protected two-qubit gates in generating entanglement. The results are complementary to current studies of entanglement protection using universal dynamical decoupling pulse sequences.

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