arXiv subjects

Md. Manirul Ali

Publications and source records attributed to Md. Manirul Ali.

33 records · Page 2Linked to original sources

arXiv2016

Nonequilibrium transient dynamics of photon statistics

We investigate the transient dynamics of photon statistics through two-time correlation functions for optical fields. We find that the transient correlations at different time t yield a smooth transition from antibunching to bunching photon statistics in the weak system-environment coupling regime. In the strong-coupling regime, the two-time correlations exhibit bunching-antibunching oscillations that persists both in the transient process and in the steady-state limit. The photon bunching-antibunching oscillations is a manifestation of strong non-Markovian dynamics, where the system remains in nonequilibrium from its environment. We also find that the antibunching to bunching transition in the weak-coupling regime and the bunching-antibunching oscillation in the strong-coupling regime are strongly influenced by the initial environment temperature.

quant-ph↗

arXiv2015

The short-time and long-time behaviors of non-Markovianity measure using two-time correlation functions in open quantum systems

We investigate non-Markovianity measure using two-time correlation functions for open quantum systems. We define non-Markovianity measure as the difference between the exact two-time correlation function and the one obtained in the Markov limit. Such non-Markovianity measure can easily be measured in experiments. We found that the non-Markovianity dynamics in different time scale crucially depends on the system-environment coupling strength and other physical parameters such as the initial temperature of the environment and the initial state of the system. In particular, we obtain the short-time and long-time behaviors of non-Markovianity for different spectral densities. We also find that the thermal fluctuation always reduce the non-Markovian memory effect. Also, the non-Markovianity measure shows non-trivial initial state dependence in different time scales.

quant-ph↗

arXiv2014

Exact decoherence dynamics of $1/f$ noise

In this paper, we investigate the exact decoherence dynamics of a superconducting resonator coupled to an electromagnetic reservoir characterized by the $1/f$ noise at finite temperature, where a full quantum description of the environment with $1/f^{x}$ noise (with $x \approx 1$) is presented. The exact master equation and the associated non-equilibrium Green's functions are solved exactly for such an open system. We show a clear signal of non-Markovian dynamics induced purely by $1/f$ noise. Our analysis is also applicable to another nano/micro mechanical oscillators. Finally, we demonstrate the non-Markovian decoherence dynamics of photon number superposition states using Wigner distribution that could be measured in experiments.

quant-ph↗

arXiv2013

Quantum Zeno dynamics of qubits in a squeezed reservoir: effect of measurement selectivity

A complete suppression of the exponential decay in a qubit (interacting with a squeezed vacuum reservoir) can be achieved by frequent measurements of adequately chosen observables. The observables and initial states (Zeno subspace) for which the effect occurs depend on the squeezing parameters of the bath. We show these_quantum Zeno dynamics_ to be substantially different for selective and non-selective measurements. In either case, the approach to the Zeno limit for a finite number of measurements is also studied numerically. The calculation is extended from one to two qubits, where we see both Zeno and anti-Zeno effects depending on the initial state. The reason for the striking differences with the situation in closed systems is discussed.

quant-ph↗

arXiv2012

A quantum effect in the classical limit: nonequilibrium tunneling in the Duffing oscillator

For suitable parameters, the classical Duffing oscillator has a known bistability in its stationary states, with low- and high-amplitude branches. As expected from the analogy with a particle in a double-well potential, transitions between these states become possible either at finite temperature, or in the quantum regime due to tunneling. In this analogy, besides local stability, one can also discuss global stability by comparing the two potential minima. For the Duffing oscillator, the stationary states emerge dynamically so that a priori, a potential-minimum criterion for them does not exist. However, global stability is still relevant, and definable as the state containing the majority population for long times, low temperature, and close to the classical limit. Further, the crossover point is the parameter value at which global stability abruptly changes from one state to the other. For the double-well model, the crossover point is defined by potential-minimum degeneracy. Given that this analogy is so effective in other respects, it is thus striking that for the Duffing oscillator, the crossover point turns out to be non-unique. Rather, none of the three aforementioned limits commute with each other, and the limiting behaviour depends on the order in which they are taken. More generally, as both $\hbar\To0$ and $T\To0$, the ratio $\hbarω_0/k_\mathrm{B}T$ continues to be a key parameter and can have any nonnegative value. This points to an apparent conceptual difference between equilibrium and nonequilibrium tunneling. We present numerical evidence by studying the pertinent quantum master equation in the photon-number basis. Independent verification and some further understanding are obtained using a semi-analytical approach in the coherent-state representation.

cond-mat.mes-hall↗

arXiv2010

Decoherence-free subspace and disentanglement dynamics for two qubits in a common non-Markovian squeezed reservoir

We study the non-Markovian entanglement dynamics of two qubits in a common squeezed bath. We see remarkable difference between the non-Markovian entanglement dynamics with its Markovian counterpart. We show that a non-Markovian decoherence free state is also decoherence free in the Markovian regime, but all the Markovian decoherence free states are not necessarily decoherence free in the non-Markovian domain. We extend our calculation from squeezed vacuum bath to squeezed thermal bath, where we see the effect of finite bath temperatures on the entanglement dynamics.

quant-ph↗

arXiv2009

Quantum interference in the time-of-flight distribution

We propose a scheme to experimentally observe matter-wave interference in the time domain, specifically in the arrival-time or the time-of-flight (TOF) distribution for atomic BEC Schrodinger-cat state represented by superposition of macroscopically separated wave packets in space. This is in contrast to interference in space at a fixed time observed in reported BEC experiments. We predict and quantify the quantum interference in the TOF distribution calculated from the modulus of the quantum probability current density (rather than the TOF distributions obtained from a purely classical or semi-classical treatment in many reported experiments). The interference and hence the coherence in the quantum TOF signal disappears in the large-mass limit. Our scheme has the potential to probe the validity of various other theoretical approaches (Phys. Rep. 338, 353 (2000)) of calculating the quantum arrival time distribution.

quant-ph↗

arXiv2007

Distinguishability of apparatus states in quantum measurement in the Stern-Gerlach experiment

In the context of the quantum mechanical modelling of a measurement process using the Stern-Gerlach setup, we critically examine the relationship between the notion of `distinguishability' of apparatus states defined in terms of the inner product and spatial separation among the emerging wave packets. We show that, in general, the mutual orthogonality of these wave packets does not necessarily imply their unambiguous spatial separation even in the asymptotic limit. A testable scheme is formulated to quantify such departures from `idealness' for a range of relevant parameters.

quant-ph↗

arXiv2007

Quantum time of flight distribution for cold trapped atoms

The time of flight distribution for a cloud of cold atoms falling freely under gravity is considered. We generalise the probability current density approach to calculate the quantum arrival time distribution for the mixed state describing the Maxwell-Boltzmann distribution of velocities for the falling atoms. We find an empirically testable difference between the time of flight distribution calculated using the quantum probability current and that obtained from a purely classical treatment which is usually employed in analysing time of flight measurements. The classical time of flight distribution matches with the quantum distribution in the large mass and high temperature limits.

quant-ph↗

arXiv2006

The Quantum-Classical Comparison of the Arrival Time Distribution through the Probability Current

We consider the arrival time distribution defined through the quantum probability current for a Gaussian wave packet representing free particles in quantum mechanics in order to explore the issue of the classical limit of arrival time. We formulate the classical analogue of the arrival time distribution for an ensemble of free particles represented by a phase space distribution function evolving under the classical Liouville's equation. The classical probability current so constructed matches with the quantum probability current in the limit of minimum uncertainty. Further, it is possible to show in general that smooth transitions from the quantum mechanical probability current and the mean arrival time to their respective classical values are obtained in the limit of large mass of the particles.

quant-ph↗

arXiv2006

Observability of the arrival time distribution using spin-rotator as a quantum clock

An experimentally realizable scheme is formulated which can test any postulated quantum mechanical approach for calculating the arrival time distribution. This is specifically illustrated by using the modulus of the probability current density for calculating the arrival time distribution of spin-1/2 neutral particles at the exit point of a spin-rotator(SR) which contains a constant magnetic field. Such a calculated time distribution is then used for evaluating the distribution of spin orientations along different directions for these particles emerging from the SR. Based on this, the result of spin measurement along any arbitrary direction for such an ensemble is predicted.

quant-ph↗

arXiv2006

On the quantum analogue of Galileo's leaning tower experiment

The quantum analogue of Galileo's leaning tower experiment is revisited using wave packets evolving under the gravitational potential. We first calculate the position detection probabilities for particles projected upwards against gravity around the classical turning point and also around the point of initial projection, which exhibit mass dependence at both these points. We then compute the mean arrival time of freely falling particles using the quantum probability current, which also turns out to be mass dependent. The mass dependence of both the position detection probabilities and the mean arrival time vanish in the limit of large mass. Thus, compatibility between the weak equivalence principle and quantum mechanics is recovered in the macroscopic limit of the latter.

quant-ph↗

arXiv2003

Spin dependent observable effect for free particles using the arrival time distribution

The mean arrival time of free particles is computed using the quantum probability current. This is uniquely determined in the non-relativistic limit of Dirac equation, although the Schroedinger probability current has an inherent non-uniqueness. Since the Dirac probability current involves a spin-dependent term, an arrival time distribution based on the probability current shows an observable spin-dependent effect, even for free particles. This arises essentially from relativistic quantum dynamics, but persists even in the non-relativistic regime.

quant-ph↗

arXiv2002

Optimal asymmetric cloning machine on a great circle using no-signalling condition

Assuming the condition of no superluminal signalling, we got an upper bound on the quality of all asymmetric $ 1\to 2$ cloning machines, acting on qubits whose Bloch vectors lie on a great circle. Then we constructed an $ 1\to 2$ cloning machine, which asymmetrically clone all qubits corresponding to this great circle, and this machine matches with that upper bound, and hence this is optimal one.

quant-ph↗

arXiv2002

Understanding Quantum Superarrivals using the Bohmian model

We investigate the orgin of ``quantum superarrivals'' in the reflection and transmission probabilities of a Gaussian wave packet for a rectangular potential barrier while it is perturbed by either reducing or increasing its height. There exists a finite time interval during which the probability of reflection is {\it larger} (superarrivals) while the barrier is {\it lowered} compared to the unperturbed case. Similarly, during a certain interval of time, the probability of transmission while the barrier is {\it raised} {\it exceeds} that for free propagation. We compute {\it particle trajectories} using the Bohmian model of quantum mechanics in order to understand {\it how} this phenomenon of superarrivals occurs.

quant-ph↗