arXiv subjects

Anirban Pathak

Publications and source records attributed to Anirban Pathak.

155 records · Page 9Linked to original sources

arXiv2009

Generalized structure of higher order nonclassicality

A generalized notion of higher order nonclassicality (in terms of higher order moments) is introduced. Under this generalized framework of higher order nonclassicality, conditions of higher order squeezing and higher order subpoissonian photon statistics are derived. A simpler form of the Hong-Mandel higher order squeezing criterion is derived under this framework by using an operator ordering theorem introduced by us in [J. Phys. A. 33 (2000) 5607]. It is also generalized for multi-photon Bose operators of Brandt and Greenberg. Similarly, condition for higher order subpoissonian photon statistics is derived by normal ordering of higher powers of number operator. Further, with the help of simple density matrices, it is shown that the higher order antibunching (HOA) and higher order subpoissonian photon statistics (HOSPS) are not the manifestation of the same phenomenon and consequently it is incorrect to use the condition of HOA as a test of HOSPS. It is also shown that the HOA and HOSPS may exist even in absence of the corresponding lower order phenomenon. Binomial state, nonlinear first order excited squeezed state (NLESS) and nonlinear vacuum squeezed state (NLVSS) are used as examples of quantum state and it is shown that these states may show higher order nonclssical characteristics. It is observed that the Binomial state which is always antibunched, is not always higher order squeezed and NLVSS which shows higher order squeezing does not show HOSPS and HOA. The opposite is observed in NLESS and consequently it is established that the HOSPS and HOS are two independent signatures of higher order nonclassicality

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arXiv2008

Reduction of Quantum Phase Fluctuations in Intermediate States

Recently we have shown that the reduction of the Carruthers-Nieto symmetric quantum phase fluctuation parameter (U) with respect to its coherent state value corresponds to an antibunched state, but the converse is not true. Consequently reduction of U is a stronger criterion of nonclassicality than the lowest order antibunching. Here we have studied the possibilities of reduction of $U$ in intermediate states by using the Barnett Pegg formalism. We have shown that the reduction of phase fluctuation parameter U can be seen in different intermediate states, such as binomial state, generalized binomial state, hypergeometric state, negative binomial state, and photon added coherent state. It is also shown that the depth of nonclassicality can be controlled by various parameters related to intermediate states. Further, we have provided specific examples of antibunched states, for which $U$ is greater than its poissonian state value.

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arXiv2007

On the Synthesis of Sequential Reversible Circuit

Reversible circuits for SR flip flop, JK flip flop, D flip flop, T flip flop, Master Slave D flip flop and Master Slave JK flip flop have been provided with three different logical approaches. All the circuits have been optimized with the help of existing local optimization algorithms (e.g. template matching, moving rule and deletion rule) and the optimized sequential circuits have been compared with the earlier proposals for the same. It has been shown that the present proposals have lower gate complexities and lower number of garbage bits compared to the earlier proposals. It has also been shown that the advantage in gate count obtained in some of the earlier proposals by introduction of New gates is an \textcolor{black}{artifact} and if it is allowed then every circuit block (unless there is a measurement) can be reduced to a single gate. Further, it is shown that a reversible flip flop can be constructed even without a feedback. In this context, some important conceptual issues related to the designing and optimization of sequential reversible circuits have also been addressed.

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arXiv2007

A mathematical criterion for single photon sources used in quantum cryptography

A single photon source (SPS) is very important for quantum computation. In particular, it is essential for secured quantum cryptography. But there is no perfect SPS in reality. Therefore, probabilistic SPS where probability of simultaneous emission of two, three, four and more photon is less than the emission of a single photon are used. Since classical photon always comes in bunch, the required single photon source must be nonclassical. In the well-known antibunched state the rate of simultaneous emission of two photon is less than that of single photon. But the requirement of quantum cryptography is a multiphoton version of the antibunched state or the higher order antibunched state. Recently we have reported a mathematical criterion for higher order antibunching. Here we have shown that any proposal for SPS to be used in quantum cryptography should satisfy this criterion. We have studied four wave mixing as a possible candidate of single photon source.

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arXiv2007

Generation of higher order nonclassical states via interaction of intense electromagnetic field with third order nonlinear medium

Interaction of intense laser beam with an inversion symmetric third order nonlinear medium is modeled as a quartic anharmonic oscillator. A first order operator solution of the model Hamiltonian is used to study the possibilities of generation of higher order nonclassical states. It is found that the higher order squeezed and higher order antibunched states can be produced by this interaction. It is also shown that the higher order nonclassical states may appear separately, i.e. a higher order antibunched state is not essentially higher order squeezed state and vice versa.

quant-ph↗

arXiv2007

Reduction of Quantum Phase Fluctuations Implies Antibunching of Photon

A clear physical meaning of the Carruthers-Nieto symmetric quantum phase fluctuation parameter (U) has been provided in Susskind Glogower and Barnett Pegg formalism of quantum phase and it is shown that the reduction of phase fluctuation parameter U with respect to its coherent state value corresponds to an antibunched state. Thus nonclassicality of a state may be manifested through the phase fluctuation parameters. As examples, quantum phase fluctuations in different optical processes, such as four wave mixing, six wave mixing and second harmonic generation have been studied by using Carruthers-Nieto quantum phase fluctuation parameters. The operators required for the calculation of quantum phase fluctuations are expressed in closed analytical forms (up to second order in coupling constant). It is also found that the reduction of phase fluctuations compared to their initial values are possible in all three cases which means nonclassical (antibunched) state exists in all these cases.

quant-ph↗

arXiv2005

Higher order antibunching is not a rare phenomenon

Since the introduction of higher order nonclassical effects, higher order squeezing has been reported in a number of different physical systems but higher order antibunching is predicted only in three particular cases. In the present work, we have shown that the higher order antibunching is not a rare phenomenon rather it can be seen in many simple optical processes. To establish our claim, we have shown it in six wave mixing process, four wave mixing process and in second harmonic generation process.

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arXiv2002

Quantum fluctations of coherent light in nonlinear media

The interaction of coherent light with a nonlinear medium is modeled here by a general quantum anharmonic oscillator. The model is not exactly solvable in a closed analytical form. But we need operator solutions of the equations of motion corresponding to these models in order to study the quantum fluctuations of coherent light in nonlinear media. In the present work we derive approximate operator solutions. From these solutions we observe that there exists an apparent discrepancy between the solutions obtained by different techniques. We compare different solutions and conclude that all correct solutions are equivalent and the apparent discrepancy is due to the use of different ordering of the operators. We use these solutions to investigate the possibilities of observing different optical phenomena in a nonlinear dielectric medium. To be precise, we have studied quantum phase fluctuations of coherent light in a third order inversion symmetric nonlinear medium. Fluctuations in phase space quadrature for the same system are studied and the possibility of generating squeezed state is reported. Fluctuations in photon number are studied and the nonclassical phenomenon of antibunching is predicted. We have generalized the results obtained for third order nonlinear medium and have studied the interaction of an intense laser beam with a general (m-1)-th order nonlinear medium. Aharanov Anandan nonadiabatic geometric phase is also discussed in the context of (m-1)-th order nonlinear medium.

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arXiv2002

Classical and Quantum Oscillators of Sextic and Octic Anharmonicities

Classical oscillators of sextic and octic anharmonicities are solved analytically up to the linear power of λ(Anharmonic Constant) by using Taylor series method. These solutions exhibit the presence of secular terms which are summed up for all orders. The frequency shifts of the oscillators for small anharmonic constants are obtained. It is found that the calculated shifts agree nicely with the available results to-date. The solutions for classical anharmonic oscillators are used to obtain the solutions corresponding to quantum anharmonic oscillators by imposing fundamental commutation relations between position and momentum operators.

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arXiv2002

Generalised quantum anharmonic oscillator using an operator ordering approach

We construct a generalised expression for the normal ordering of (a+a^{\dagger})^{m} for integral values of m and use the result to study the quantum anharmonic oscillator problem in the Heisenberg approach. In particular, we derive generalised expressions for energy eigen values and frequency shifts for the Hamiltonian H=\frac{x^{2}}{2}+\frac{\dot{x}^{2}}{2}+\fracλ{m}x^{m}. We also derive a closed form first order multi scale perturbation theoretic operator solution of this Hamiltonian with a view to generalise some recent results of Bender and Bettencourt .

math-ph↗

arXiv2002

Aharanov Anandan Phase for the Quasi Exactly Solvable Bose Systems

An extended notion of quasi-exactly solvable potential model is used here to treat quasi exactly solvable (QES) Bose systems. We report an analytic expression for the Ahoronov Anandan non-adiabatic geometric phase for the QES Bose system in general. The generalized expression is then used to study some particular cases of physical interest and we observe that the geometric phase can be tuned.

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