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The ultrastrong coupling between the elementary excitations of matter and microcavity modes is studied in a fully analytical quantum-mechanical theoretical framework. The elementary excitation could be phonons, excitons, plasmons, etc. From the diagonalization of the Hamiltonian, we obtain the ground state of the polariton Hamiltonian. The ground state belongs to the Gaussian class. Using the Gaussian property we calculate the quantum entanglement in the ground state. We use two different measures for quantum entanglement -- entanglement entropy and the logarithmic negativity parameter and obtain rather simple analytical expressions for the entanglement measures. Our findings show that the amount of quantum entanglement in the ground state is quite significant in the ultrastrong coupling regime. It can be obtained from the measurement of the polariton frequencies.

We study the heat transfer between N coupled quantum resonators with applied synthetic electric and magnetic fields realized by changing the resonators parameters by external drivings. To this end we develop two general methods, based on the quantum optical master equation and on the Langevin equation for $N$ coupled oscillators where all quantum oscillators can have their own heat baths. The synthetic electric and magnetic fields are generated by a dynamical modulation of the oscillator resonance with a given phase. Using Floquet theory we solve the dynamical equations with both methods which allow us to determine the heat flux spectra and the transferred power. With apply these methods to study the specific case of a linear tight-binding chain of four quantum coupled resonators. We find that in that case, in addition to a non-reciprocal heat flux spectrum already predicted in previous investigations, the synthetic fields induce here non-reciprocity in the total heat flux hence realizing a net heat flux rectification.

We present a new paradigm in the field of cavity QED by bringing out remarkable features associated with the avoided crossing of the dressed state levels of the Jaynes Cummings model. We demonstrate how the parametric couplings, realized by a second order nonlinearity in the cavity, can turn the crossing of dressed states into avoided crossings. We show how one can generate coherence between the avoided crossing of dressed states. Such coherences result, for example, in quantum beats in the excitation probability of the qubit. The quality of quantum beats can be considerably improved by adiabatically turning on the parametric interaction. We show how these avoided crossings can be used to generate superpositions of even or odd Fock states with the remarkable property of equal weights for the states in superposition. The fidelity of generation is more than 95\%. In addition, we show strong entanglement between the cavity field and the qubit with the concurrence parameter exceeding 90\%.

We study wave-particle duality by exploring for the first time effects of a quantum object's source. A single photon emitted from a pair of nonlocally entangled two-level atoms is specifically analyzed. Surprisingly, duality is found to be a conditional phenomenon depending on the photon's atomic source. It can be tuned maximum, medium, and even minimum (completely absent) by the atomic state purity through an exact quadratic relation that can be called Duality Pythagorean Theorem. The analysis shows a new way of investigating duality by accounting how the single quantum object is created. The result sheds a new light on the fundamental understanding of the completeness of wave-particle duality, and can be tested in various practical physical systems., 5 pages, 2 figures

We investigate the cavity excitation spectrum and the photon number distribution in a cavity QED system driven by a broadband squeezed vacuum. In an empty cavity, we show that only states with even number of photons can be measured under resonant condition since the squeezed vacuum consists of states with even number of photons only. When a single atom is trapped in the cavity, the strong coupling between the atom and cavity results in energy splittings of the system, and there exist two peaks in the cavity excitation spectrum at two-photon transition frequencies. At the central frequency, however, all photon states can be detected because of the interaction between the atom and cavity. Therefore, it can be used to detect whether a single atom is trapped in the cavity. We also show that the squeezed vacuum can promote multiphoton excitations in the cavity. Using a coherent probe field, it is possible to explore higher Jaynes-Cummings doublet even if the probe field intensity is very weak.

Currently epsilon near zero materials (ENZ) have become important for controlling the propagation of light and enhancing by several orders of magnitude the Kerr and other nonlinearities. Given this advance it is important to examine the quantum electrodynamic processes and information tasks near ENZ materials. We study the entanglement between two two-level systems near ENZ materials and compare our results with the case where the ENZ material is replaced by a metal. It is shown that with ENZ materials substantial entanglement can be achieved over larger distances than for metal films. We show that this entanglement over large distances is due to the fact that one can not only have large emission rates but also large energy transmission rates at the epsilon-nearzero wavelength. This establishes superiority of ENZ materials for studying processes specifically important for quantum information tasks.

Using Maxwell-Bloch equations it has been shown how the superradiance can lead to amplification and gain at a frequency much larger than the pumping frequency. This remarkable effect has been examined in terms of a simpler model involving two coupled oscillators with one of them paramet- rically driven. We show that this coupled oscillator model has a hidden parity-time (PT) symmetry for QASER, we thus bring PT symmetry to the realm of parametrically coupled resonators. More- over, we find that the QASER gain arises from the broken PT symmetry phase. We then quantize the simplified version of the QASER using quantum Langevin equations. The quantum description enables us to understand how the system starts from quantum fluctuations.

Vacuum induced coherence in a strongly coupled cavity consisting of a three-level system is studied theoretically. The effects of the strong coupling to electromagnetic field vacuum are examined by solution of an open-system quantum master equation. The numerical results show that the system exhibits population trapping, and the numerical results are interpreted with analytical expressions derived from a new basis in the weak excitation regime. We further show that the generated effects can be probed with weak external fields. Moreover, it is shown that the induced coherence can be controlled by the applied field parameters like field detuning. Finally, we study the trapping dynamics in the strong field excitation regime, and also demonstrate that a recently proposed asymmetric pumping regime (limited to the weak coupling regime) can remove the radiative decay of coherent Rabi oscillations, with both weak and strong excitation fields.

We examine the fluctuation theorems which traditionally have been studied for classical systems and enquire if they can be extended to the quantum domain, especially at low temperatures. The example chosen is that of a problem which has proven to be of great interest in the context of Landau diamagnetism viz. the quantized motion of an electron in a magnetic field and in a dissipative environment. It is established from first principles that the quantum work operator W has a Gaussian distribution even though the system under consideration has a four dimensional phase space. The parameter $\alpha$ in the fluctuation theorem $p(W )/p(-W) = exp(\alpha W)$ depends on the system dynamics and has characteristic quantum features, especially at low temperatures. Certain unique low temperature signatures are also discussed., Comment: 13 pages

In the light of the interest in the transport of single photons in arrays of waveguides, fiber couplers, photonic crystals, etc., we consider the quantum mechanical process of the tunneling of photons through evanescently or otherwise coupled structures. We specifically examine the issue of tunneling between two structures when one structure already contains few photons. We demonstrate the possibility of both photon aided and inhibited tunneling of photons. The Bosonic nature of photons enhances the tunneling probability. We also show how the multiphoton tunneling probability can be either enhanced or inhibited due to the presence of photons. We find similar results for the higher order tunneling. Finally, we show that the presence of a squeezed field changes the nature of tunneling considerably.

We present a self contained formalism modelled after the Brownian motion of a quantum harmonic oscillator for describing the performance of microscopic Brownian heat engines like Carnot, Stirling and Otto engines. Our theory, besides reproducing the standard thermodynamics results in the steady state enables permits us to study the role dissipation plays in determining the efficiency of Brownian heat engines under actual laboratory conditions. In particular, we analyse in detail the dynamics associated with decoupling a system in equilibrium with one bath and recoupling it to another bath and obtain exact analytical results which are shown to have significant ramifications on the efficiencies of engines involving such a step. We also develop a simple yet powerful technique for computing corrections to the steady state results arising from finite operation time and use it to arrive at the thermodynamic complementarity relations for various operating conditions and also to compute the efficiencies of the three engines cited above at maximum power. Some of the methods and techniques and exactly solvable models presented here are interesting in their own right and, in our opinion, would find useful applications in other contexts as well., Comment: Latex, 18 pages, 2 Figure

We show the existence of a very large spin Hall effect of light (SHEL) in single photon plasmonics based on spontaneous emission and the dipole-dipole interaction initiated energy transfer (FRET) on plasmonic platforms. The spin orbit coupling inherent in Maxwell equations is seen in the conversion of sigma + photon to sigma - photon. The FRET is mediated by the resonant surface plasmons and hence we find very large SHEL. We present explicit results for SHEL on both graphene and metal films. We also study how the splitting of the surface plasmon on a metal film affects the SHEL. In contrast to most other works which deal with SHEL as correction to the paraxial results, we consider SHEL in the near field of dipoles which are far from paraxial.

We present a technique based on multi-photon detection which leads to a strong focussing of photons scattered by independent single photon emitters. For N single photon sources it is shown that if m - 1 photons are detected in a particular direction (with m \leq N) the probability to detect the m-th photon in the same direction can be as high as 100%. This measurement induced focussing effect is already clearly visible for m>2., 4 pages, 2 figures

Using electromagnetically induced transparency we show how the opto-mechanical systems can be used both as memory elements as well as for the transduction of optical fields. We use a double cavity optomechanical system which facilitates such applications. By tuning the frequency of the second cavity one can produce output fields at a variety of frequencies. We present analytical results for the steady state behavior which is controlled by the power and the detuning of the field driving the second cavity.

We show how to prepare and directly measure the squeezed states of nanomechanical oscillators. An intense pulse interacts with a dielectric mirror in a cavity. The quadratic coupling between the optical pulse and the oscillator results in the reduction of a quadrature variance of the massive oscillator. Differently from others, the proposed scheme here requires neither any post-action on the optical field nor a preparation of a nonclassical optical field. Depending on the initial temperature of the system, the squeezing of the variance under the vacuum limit can be achieved only by a few repetitive interactions., 4 pages, 1 figures

A theoretical realization of an all-optical quantum ratchet is proposed in a medium composed of an array of coupled waveguides. By coupling light into two adjacent waveguides, and calculating the expectation value for the position space operator, we demonstrate the quantum ratchet like behavior of this optical system.

Dissipation is generally thought to affect the quantum nature of the system in an adverse manner, however we show that dissipatively coupled nano systems can be prepared in states which beat the standard quantum limit of the mechanical motion. We show that the reactive coupling between the waveguide and the microdisk resonator can generate the squeezing of the waveguide by injecting a quantum field and laser into the resonator through the waveguide. The waveguide can show about 70--75% of maximal squeezing for temperature about 1--10 mK. The maximum squeezing can be achieved with incident pump power of only 12 $\mu$W for a temperature of about 1 mK. Even for temperatures of 20 mK, achievable by dilution refrigerators, the maximum squeezing is about 60%., Comment: 6 pages,2 figures

We demonstrate that intensity correlations of second order in the fluorescence light of N > 2 single- photon emitters may violate locality while the visibility of the signal remains below 71%. For this, we derive a homogeneous Bell-Wigner-type inequality, which can be applied to a broad class of experimental setups. We trace the violation of this inequality back to path entanglement created by the process of detection., 9 pages, 5 figures

We present in this letter a scheme for optical interferometry. We utilize coherent-beam-stimulated two-mode squeezed light, which interacts with a phase shifter and is then squeezed again before detection. Our theoretical device has the potential to reach far below the shot noise limit (SNL) in phase sensitivity. This new proposal avoids the pitfalls of other setups, such as difficulty in creating the required resource. Furthermore, our scheme requires no complicated detection protocol, relying instead only on simple intensity measurement. Also, bright, coherent sources "boost" squeezed light, creating a very sensitive device. This hybrid scheme relies on no unknown components and can be constructed with current technology. In the following we present our analysis of this relatively straightforward device, using the operator propagation method. We derive the phase sensitivity and provide a simple numerical example of the power of our new proposal. Sensitivity scales as a shot noise limited Mach-Zehnder Interferometer, multiplied by a sub-Heisenberg contribution from the squeezed light., 10 pages, 4 figures, Same as published in NJP

We show that squeezing of a nanomechanical mirror can be generated by injecting broad band squeezed vacuum light and laser light into the cavity. We work in the resolved sideband regime. We find that in order to obtain the maximum momentum squeezing of the movable mirror, the squeezing parameter of the input light should be about 1. We can obtain more than 70% squeezing. Besides, for a fixed squeezing parameter, decreasing the temperature of the environment or increasing the laser power increases the momentum squeezing. We find very large squeezing with respect to thermal fluctuations, for instance at 1 mK, the momentum fluctuations go down by a factor more than one hundred., 6 pages,5 figures

We examine the question of survival of quantum entanglement between the bipartite states and multiparticle states like GHZ states under the action of a dephasing bath by the application of sequence of $��$ pulses. We show the great advantage of the pulse sequence of Uhrig [ 2007 {\it Phys. Rev. Lett.} {\bf 98} 100504] applied at irregular intervals of time, in controlling quantum entanglement. In particular death of entanglement could be considerably delayed by pulses. We use quantum optical techniques to obtain exact results., 5 pages, 3 figures

We investigate the viability of coupled waveguides as basic units of quantum circuits. In particular, we study the dynamics of entanglement for the single photon state, and single mode squeezed vacuum state. We further consider the case of entangled inputs in terms of the two mode mode squeezed vacuum states and the two photon NOON state. We present explicit analytical results for the measure of entanglement in terms of the logarithmic negativity. We also address the effect of loss on entanglement dynamics of waveguide modes. Our results indicate that the waveguide structures are reasonably robust against the effect of loss and thus quite appropriate for quantum architectures as well as for the study of coherent phenomena like random walks. Our analysis is based on realistic structures used currently., Comment: 9 pages, 10 figures

We present a coherent population trapping based scheme to attain sub-nanoscale resolution for atom localization, microscopy and lithography. Our method uses three-level atoms coupled to amplitude modulated probe field and spatially dependent drive field. The modulation of the probe field allows us to tap into the steep dispersion normally associated with electromagnetically induced transparency and offers an avenue to attain sub-nanometer resolution using just optical fields. We illustrate application of the techniques to the area of microscopy and lithography and show how multilevel schemes offer the possibility of improving resolution further., Comment: submitted

We examine the behavior of a Non Gaussian state like NOON state under phase insensitive amplification. We derive analytical result for the density matrix of the NOON state for arbitrary gain of the amplifier. We consider cases of both symmetric and antisymmetric amplification of the two modes of the NOON state. We quantitatively evaluate the loss of entanglement by the amplifier in terms of the logarithmic negativity parameter. We find that NOON states are more robust than their Gaussian counterparts., Comment: 5 pages, 2 figures

We consider an array of coupled optical cavities, each containing a multi-atom ensemble. We show that the nonlinearity inherent in the cooperative dynamics of the atoms in each ensemble coupled to the respective cavity field allows for the formation of solitary waves. Such a prediction can be tested in state-of-the-art semiconducting photonic-crystal microcavities with embedded impurities., Comment: 4 pages, two figures, RevTeX4

The first optical proposal for the realization of the two-bit version of the Deutsch-Jozsa algorithm [D. Deutsch and R. Jozsa, Proc. R. Soc. London A {\bf 493}, 553 (1992)] is presented. The proposal uses Stark shifts in an ensemble of atoms and degenerate sources of photons. The photons interact dispersively with an atomic ensemble, leading to an effective Hamiltonian in atom-field basis, which is useful for performing the required two-qubit operations. Combining these with a set of one-qubit operations, the algorithm can be implemented. A discussion of the experimental feasibility of the proposal is given., 9 pages, 3 figures, 1 table, IOP, submitted

We study the quantum properties of a nanomechanical oscillator via the squeezing of the oscillator amplitude. The static longitudinal compressive force $F_0$ close to a critical value at the Euler buckling instability leads to an anharmonic term in the Hamiltonian and thus the squeezing properties of the nanomechanical oscillator are to be obtained from the Hamiltonian of the form $H= a^{\dag}a+\beta (a^{\dag}+a)^4/4$. This Hamiltonian has no exact solution unlike the other known models of nonlinear interactions of the forms $a^{\dag 2}a^2$, $(a^{\dag}a)^2$ and $a^{\dag4}+a^4-(a^{\dag2}a^2+a^2a^{\dag2})$ previously employed in quantum optics to study squeezing. Here we solve the Schr\"odinger equation numerically and show that in-phase quadrature gets squeezed for both ground state and coherent states. The squeezing can be controlled by bringing $F_0$ close to or far from the critical value $F_c$. We further study the effect of the transverse driving force on the squeezing in nanomechanical oscillator., Comment: 8 pages, 7 figures, 1 table

We investigate whether it is possible to store and retrieve the intense probe pulse from a $\Lambda$-type homogeneous medium of cold atoms. Through numerical simulations we show that it is possible to store and retrieve the probe pulse which are not necessarily weak. As the intensity of the probe pulse increases, the retrieved pulse remains a replica of the original pulse, however there is overall broadening and loss of the intensity. These effects can be understood in terms of the dependence of absorption on the intensity of the probe. We include the dynamics of the control field, which becomes especially important as the intensity of the probe pulse increases. We use the theory of adiabatons [Grobe {\it et al.} Phys. Rev. Lett. {\bf 73}, 3183 (1994)] to understand the storage and retrieval of light pulses at moderate powers., Comment: 15 pages, 7 figures, typed in RevTex

We present a brief review of the impact of the Heisenberg uncertainty relations on quantum optics. In particular we demonstrate how almost all coherent and nonclassical states of quantum optics can be derived from uncertainty relations., Comment: Lecture given at the Heisenberg Centenary Symposium, Bamberg, Germany, September 2001, 8 pages, 1 figure

We show that it is possible to entangle three different many-particle states by Bragg spectroscopy with nonclassical light in a Bose condensate of weakly interacting atomic gases. Among these three states, two are of atoms corresponding to two opposite momentum side-modes of the condensate; and the other is of single-mode photons of the output probe beam. We demonstrate strong dependence of the multiparticle entanglement on the quantum statistics of the probe light. We present detailed results on entanglement keeping in view of the possible experimental situation., 5 pages, 4 figures, Revtex

We point out the relation between the work of Zheng and ours, APS [G.S. Agarwal, R.R. Puri, and R.P. Singh, Phys. Rev. A 56, 2249 (2001)] and show the important connection between the atomic cat state and the GHZ states., Comment: one page, submitted to PRL

We show how the application of a coupling field connecting the two lower metastable states of a Lambda system facilitates stoppage of light in a coheren tly driven Doppler broadened atomic medium via electromagnetic induced transparency, Comment: 11 pages, 3 figures, typed in Latex, Accepted in JMO

We examine the feasibility of enhancing the fundamental radiative interactions between distant atoms. We present general arguments for producing enhancement. In particular, we show how giant dipole-dipole interaction can be produced by considering dipoles placed close to micron sized silica spheres. The giant interaction arises as the whispering gallery modes can resonantly couple the dipoles., 4 figures included in the postscript file, to appear in "Current trens in Atomic and Molecular Physics", edited by R. Srivastava (Phoenix publishing House, New Delhi, India, 2001)

The fidelity of quantum cloning is very often limited by the accompanying unwanted transitions. We show how the fidelity can be improved by using a coherent field to cycle away the unwanted transitions. We demonstrate this explicitly in the context of the model of Simon {\it et al.} [J. Mod. Opt. {\bf 47}, 233 (2000) ; Phys. Rev. Lett. {\bf 84}, 2993 (2000)]. We also investigate the effects of the number of atoms on the quality of quantum cloning. We show that the universality of the scheme can be maintained by choosing the cycling field according to the input state of the qubit., RevTeX, 12 pages, 6 figures, the text has been thoroughly revised with modified abstract, new figures and added reference ; resubmitted to Phys. Rev. A

The paper has been withdrawn by authors., Comment: paper withdrawn

An isotropic medium, having magnetic sublevels, when subjected to a magnetic field or an electromagnetic field can induce anisotropy in the medium; and as a result the plane of polarization of the probe field can rotate. Therefore the rotation due to the magnetic field alone, can be {\em controlled efficiently} with use of a coherent field. We show, using a control field, significant enhancement of the magneto-optical rotation and demonstrate the possibility of realizing {\em magneto-optical switch}., 5 pages, 3 figures, style files included

We propose a simple test to demonstrate and detect the presence of vacuum inducde coherence in a $��$-system. We show that the probe field absorption is modulated due to the presence of such a coherence which is unobservable in fluorescence. We present analytical and numerical results for the modulated absorption, the cosine and sine components of which display different types of behavior., 9 pages, 4 postscript files. Submitted for the special issue of "Laser Physics" on "Lasing without inversion and Interference phenomena in Atomic systems", Vol 9, #3, 1999

We introduce and study the properties of a class of coherent states for the group SU(1,1) X SU(1,1) and derive explicit expressions for these using the Clebsch-Gordan algebra for the SU(1,1) group. We restrict ourselves to the discrete series representations of SU(1,1). These are the generalization of the `Barut Girardello' coherent states to the Kronecker Product of two non-compact groups.The resolution of the identity and the analytic phase space representation of these states is presented. This phase space representation is based on the basis of products of `pair coherent states' rather than the standard number state canonical basis. We discuss the utility of the resulting `bi-pair coherent states' in the context of four-mode interactions in quantum optics., Comment: 7 pages, 2 figures (can be obtained from author by snail mail)

A new proof for the completeness of the coherent states $D(��)\mid f>$ for the Heisenberg Weyl group and the groups $SU(2)$ and $SU(1,1)$ is presented. Generalizations of these results and their consequences are disussed., 10 pages, latex, no figures