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A. K. Rajagopal

Publications and source records attributed to A. K. Rajagopal.

At least 55 records · Page 3Linked to original sources

Quantum Mechanical Basis of Vision

The two striking components of retina, i.e., the light sensitive neural layer in the eye, by which it responds to light are (the three types of) color sensitive Cones and color insensitive Rods (which outnumber the cones 20:1). The interaction between electromagnetic radiation and these photoreceptors (causing transitions between cis- and trans- states of rhodopsin molecules in the latter) offers a prime example of physical processes at the nano-bio interface. After a brief review of the basic facts about vision, we propose a quantum mechanical model (paralleling the Jaynes-Cummings model (JCM) of interaction of light with matter) of early vision describing the interaction of light with the two states of rhodopsin mentioned above. Here we model the early essential steps in vision incorporating, separately, the two well-known features of retinal transduction (converting light to neural signals): small numbers of cones respond to bright light (large number of photons) and large numbers of rods respond to faint light (small number of photons) with an amplification scheme. An outline of the method of solution of these respective models based on quantum density matrix is also indicated. This includes a brief overview of the theory, based on JCM, of signal amplification required for the perception of faint light. We envision this methodology, which brings a novel quantum approach to modeling neural activity, to be a useful paradigm in developing a better understanding of key visual processes than is possible with currently available models that completely ignore quantum effects at the relevant neural level.

q-bio.NC↗

Generalized information theoretic measure to discern the quantumness of correlations

A novel measure, quantumness of correlations is introduced here for bipartite states, by incorporating the required measurement scheme crucial in defining any such quantity. Quantumness coincides with the previously proposed measures in special cases and it vanishes for separable states - a feature not captured by the measures proposed earlier. It is found that an optimal generalized measurement on one of the parts leaves the overall state in its closest separable form, which shares the same marginal for the other part, implying that quantumness is non-zero for all entangled bipartite states and it serves as an upper bound to the relative entropy of entanglement.

quant-ph↗

Distinctive features in the quantum sub-dynamics of bipartite systems

Distinctive features in the sub-dynamics of an interacting bipartite system are explored. The sub-dynamic Heisenberg operators are introduced in a novel way leading to the quasi-particle-like concept in the respective subsystems. This formulation is illustrated using the known exact solutions of the generic (Jaynes - Cummings) model of interacting bipartite system of a spin 1/2 particle and a single mode electromagnetic field (more generally, boson field). The striking effects of interaction and entanglement are reflected in the dressing of the non-interacting number and spin representations, displaying quasi-particle-like properties. This development may be at the heart of the physics of back - action discussed in the recent literature.

quant-ph↗

Collective multipole-like signatures of entanglement in symmetric N-qubit systems

A cogent theory of collective multipole-like quantum correlations in symmetric multiqubit states is presented by employing SO(3) irreducible spherical tensor representation. An arbitrary bipartite division of this system leads to a family of inequalities to detect entanglement involving averages of these tensors expressed in terms of the total system angular momentum operator. Implications of this theory to the quantum nature of multipole-like correlations of all orders in the Dicke states are deduced. A selected set of examples illustrate these collective tests. Such tests detect entanglement in macroscopic atomic ensembles, where individual atoms are not accessible.

quant-ph↗

A POVM view of the ensemble approach to polarization optics

Statistical ensemble formalism of Kim, Mandel and Wolf (J. Opt. Soc. Am. A 4, 433 (1987)) offers a realistic model for characterizing the effect of stochastic non-image forming optical media on the state of polarization of transmittedlight. With suitable choice of the Jones ensemble, various Mueller transformations - some of which have been unknown so far - are deduced. It is observed that the ensemble approach is formally identical to the positive operator valued measures (POVM) on the quantum density matrix. This observation, in combination with the recent suggestion by Ahnert and Payne (Phys. Rev. A 71, 012330, (2005)) - in the context of generalized quantum measurement on single photon polarization states - that linear optics elements can be employed in setting up all possible POVMs, enables us to propose a way of realizing different types of Mueller devices.

physics.optics↗

Characterizing multiparticle entanglement in symmetric N-qubit states via negativity of covariance matrices

We show that higher order inter-group covariances involving even number of qubits are necessarily positive semidefinite for N qubit separable states, which are completely symmetric under permutations of the qubits. This identification leads to a family of sufficient conditions of inseparability based on the negativity of 2kth order inter-group covariance matrices of symmetric N-qubit systems. These conditions have a simple structure and detect entanglement in all even partitions of the symmetric multiqubit system. The observables involved are feasible experimental quantities and do not demand full state determination through quantum state tomography.

quant-ph↗

Constraints on the uncertainties of entangled symmetric qubits

We derive necessary and sufficient inseparability conditions imposed on the variance matrix of symmetric qubits. These constraints are identified by examining a structural parallelism between continuous variable states and two qubit states. Pairwise entangled symmetric multiqubit states are shown here to obey these constraints. We also bring out an elegant local invariant structure exhibited by our constraints.

quant-ph↗

Superstatistics - a quantum generalization

A quantum mechanical generalization of superstatistics is presented here based on the positive operator valued measure transformation property of the system density matrix. This procedure reveals that the origin of the fluctuating factors occurring in the derivation of the superstatistics lies in the choice of the transformation operators governing the dynamics of fluctuations. This generalization addresses situations such as nanosystems based on quantum devices (e.g., superconducting devices, single electron transistors, etc,) operating at low temperatures where cognizance of quantum fluctuations is essential.

cond-mat.mes-hall↗

Electron Spin Dynamics in a Quantum Dot due to Hyperfine Coupling with Nuclei in the Dot - An Exact Analysis

The time-dependent Schrodinger equation of a many particle spin system consisting of an electron in a quantum dot interacting with the spins of the nuclei (N) in the dot due to hyperfine interaction is solved exactly for a given arbitrary initial state. The electron spin dynamics is then expressed in terms of the reduced density matrix of the composite system by computing the marginal density matrix of the electron. This is accomplished by classifying states of the system by the total spin of the coupled electron and nuclear system that commutes with the system Hamiltonian. These states are used in enumerating and finding the exact solution of the time-dependent Schrodinger equation. In each sector of the total spin, the problem reduces to solving a linear simultaneous set of equations that are solved by matrix inversion. Such solutions enable one to make a reliable approximate scheme for purposes of numerical estimation of the various physical quantities. A methematical and physical discussion of this procedure with the density matrix approach to this problem is given here. To elucidate the procedure and its advantages, special cases of N=3,4 are given in some detail in an Appendix.

quant-ph↗

Relationship of Quantum Entanglement to Density Functional Theory

The maximum von Neumann entropy principle subject to given constraints of mean values of some physical observables determines the density matrix. Similarly the stationary action principle in the case of time-dependent (dissipative) situations under similar constraints yields the density matrix. The free energy and measures of entanglement are expressed in terms of such a density matrix and thus define respective functionals of the mean values. In the light of several model calculations, it is found that the density matrix contains information about both quantum entanglement and phase transitions even though there may not be any direct relationship implied by one on the other.

quant-ph↗

Quantum dynamics in view of Einstein's theory of Brownian motion

A quantum-mechanical version of Einstein's 1905 theory of Brownian motion is presented. Starting from the Hamiltonian dynamics of an isolated composite of objective and environmental systems, subdynamics for the objective system is derived in the spirit of Einstein. The resulting master equation is found to have the Lindblad structure.

cond-mat.other↗

Structure of the Phase in Pure Two-Mode Gaussian States

The two-mode relative phase associated with Gaussian states plays an important role in quantum information processes in optical, atomic and electronic systems. In this work, the origin and structure of the two-mode relative phase in pure Gaussian states is studied in terms of its dependences on the quadratures of the modes. This is done by constructing local canonical transformations to an associated two-mode squeezed state. The results are illustrated by studying the time dependence of the phase under a nonlocal unitary model evolution containing correlations between the modes. In a more general context, this approach may allow the two-mode phase to be studied in situations sensitive to different physical parameters within experimental configurations relevant to quantum information processing tasks.

quant-ph↗

Inconsistencies of the Adiabatic Theorem and the Berry Phase

The adiabatic theorem states that if we prepare a quantum system in one of the instantaneous eigenstates then the quantum number is an adiabatic invariant and the state at a later time is equivalent to the instantaneous eigenstate at that time apart from phase factors. Recently, Marzlin and Sanders have pointed out that this could lead to apparent violation of unitarity. We resolve the Marzlin-Sanders inconsistency within the quantum adiabatic theorem. Yet, our resolution points to another inconsistency, namely, that the cyclic as well as non-cyclic adiabatic Berry phases may vanish under strict adiabatic condition. We resolve this inconsistency and develop an unitary operator decomposition method to argue for the validity of the adiabatic approximation.

quant-ph↗

Classical Statistics Inherent in a Quantum Density Matrix

A density matrix formulation of classical bipartite correlations is constructed. This leads to an understanding of the appearance of classical statistical correlations intertwined with the quantum correlations as well as a physical underpinning of these correlations. As a byproduct of this analysis, a physical basis of the classical statistical correlations leading to additive entropy in a bipartite system discussed recently by Tsallis et al emerges as inherent classical spin fluctuations. It is found that in this example, the quantum correlations shrink the region of additivity in phase space.

quant-ph↗

Entanglement of Pure Two-Mode Gaussian States

The entanglement of general pure Gaussian two-mode states is examined in terms of the coefficients of the quadrature components of the wavefunction. The entanglement criterion and the entanglement of formation are directly evaluated as a function of these coefficients, without the need for deriving local unitary transformations. These reproduce the results of other methods for the special case of symmetric pure states which employ a relation between squeezed states and Einstein-Podolsky-Rosen correlations. The modification of the quadrature coefficients and the corresponding entanglement due to application of various optical elements is also derived.

quant-ph↗

Contractive Entanglement in Squeezed State Evolution

The position variance of a single-mode Yuen states can go below the standard quantum limit. For two-mode squeezed states, it is shown that the time-dependent evolution of the entanglement of formation can be contractive, going below that of the squeezed state with minimum Einstein-Podolsky-Rosen dispersions, and increasing thereafter. The rate of change of the Einstein-Podolsky-Rosen dispersions as a function of the two-mode phases control this process. Contractive entanglement is shown to be equivalent to a rotating phase space accompanied by time-dependent single-mode squeezing.

quant-ph↗

Nanothermodynamics:a generic approach to material properties at nanoscale

Granular and nanoscale materials containing a relatively small number of constituents have been studied to discover how their properties differ from their macroscopic counterparts. These studies are designed to test how far the known macroscopic approaches such as thermodynamics may be applicable in these cases. A brief review of the recent literature on these topics is given as a motivation to introduce a generic approach called nanothermodynamics. An important feature that must be incorporated into the theory is the non-additive property because of the importance of surface contributions to the physics of these systems. This is achieved by incorporating fluctuations into the theory right from the start. There are currently two approaches to incorporate this property. Hill (and further elaborated more recently with Chamberlin) initiated an approach by modifying the thermodynamic relations by taking into account the surface effects. We generalize Boltzmann-Gibbs statistical mechanics by relaxing the additivity properties of thermodynamic quantities to include nonextensive features of such systems. An outline of this generalization of the macroscopic thermodynamics to nano-systems will be given here.

cond-mat.stat-mech↗

Scaling relations in equilibrium nonextensive thermostatistics

The forms of Euler and Gibbs-Duhem relations discussed in thermodynamics of extensive systems are shown to hold also for nonextensive systems with long-range interactions with a novel interpretation of entities appearing therein. In this way, the principles underlying Tsallis' scaling relations in equilibrium nonextensive thermostatistics are clarified.

cond-mat.stat-mech↗