Krishna Rai Dastidar

Realization of a negative refractive index in a three-level Λ system via spontaneously generated coherence

A new scheme to realize simultaneous negative permittivity and permeability in a three-level closed ? system with incoherent pumping via spontaneously generated coherence has been presented. We have shown that the negative refractive index can be realized in a heteronuclear molecule such as LiH. The negative refractive index can be achieved in a band of frequency range. The position and the band of the frequency region of negative refraction can be manipulated by controlling the incoherent pump rate. We achieve a figure of merit (FOM) = |Re(n)/Im(n)| = 1.797 for the LiH molecule.

Control over group velocity in a three-level closed Λ system via spontaneously generated coherence and dynamically induced coherence

The light propagation of a probe field in a three-level Λ system with incoherent pumping has been studied when both dynamically induced coherence (DIC) and spontaneously generated coherence (SGC) play a significant role. We have investigated the group velocity of probe field and hence the group index of a three-level Λ system with incoherent pumping when both DIC and SGC play a significant role. We have shown that by varying the probe field Rabi frequency one can control the interference between these two coherences which leads to different nonlinear response (amplification without inversion, electromagnetically induced transparency and electromagnetically induced absorption) leading to different (positive and negative) dispersion. Hence control over switching of group velocity from subluminal to superluminal and vice versa can be achieved. We have also shown that when the contributions from both the coherences are comparable, the dependence of group velocity of probe field in a three-level Λ system with incoherent pumping on phase difference between probe and coherent fields is different from that obtained under the weak probe field condition. Going beyond the weak probe field approximation we have derived analytical expressions for group velocity and hence the group index in the steady state limit (keeping all orders of system parameters) to generalize the analysis, and these expressions can be used for any set of system parameters without any restriction. The numerical values obtained by solving the density matrix equations agree well with these exact analytical values at a large time limit. We have proposed a scheme for experimental realization of EIT and hence subluminal light propagation in molecules by invoking spontaneously generated coherence.

Combined effect of spontaneously generated coherence and dynamically induced coherence in a three-level closed Λ system

In a three-level closed Λ system with incoherent pumping, both the dynamically induced coherence (DIC) and the spontaneously generated coherence (SGC) play a significant role in inducing different nonlinear processes like amplification without population inversion (AWI), electromagnetically induced transparency (EIT) and electromagnetically induced absorption (EIA). These two coherences can interfere destructively and constructively giving rise to different nonlinear processes (EIT, EIA, AWI) when the strength of these two coherences is comparable. Therefore the system can switch over from one nonlinear process to the other and the desired response of the system can be achieved by controlling the system parameters. It has been shown that this switching can occur by changing the relative strength of Rabi frequencies for the coherent and probe fields and the mode of incoherent pumping (unidirectional and bidirectional) for a chosen SGC parameter. Further control over the response can be achieved by changing the phase between two radiation fields. But the dependence on phase is different when both the coherences contribute than that obtained only from SGC. Exact analytical expressions for the coherences and populations in the steady state limit have been derived (keeping all orders of system parameters) to generalize the analysis and any restrictions over the system parameters (e.g. spontaneous decay widths on probe and coherent transitions are equal) have been avoided to make it applicable to various atomic and molecular systems. However the approximate expressions can be derived from these exact values. Numerical values obtained by solving the density matrix equations agreed well with these exact analytical values.

Control of (1+1′)-photon dissociation in NaH

We have studied -photon dissociation of the NaH molecule (ab initio) from the v = 0 level of the ground electronic state (X 1Σ+) to the repulsive B 1Π state via the bound intermediate A 1Σ+ state. By solving the one-dimensional time-dependent Schrodinger equation for nuclear motion using the Fourier grid technique we have shown that the maximum of the -photon dissociation cross section and the shape of the dissociation spectrum can be controlled by controlling the time delay between the two photoexcitation processes, i.e. bound–bound excitation by the first photon and bound–continuum excitation by the second photon respectively. The oscillation of the maximum of the dissociation cross section with time delay between the two pulses has been shown to be due to the excitation of different oscillating wavepackets at different delays from the intermediate A 1Σ+ state. It has also been shown that the dissociation spectrum depends on the duration and temporal profile of the femtosecond pulses used for excitation and hence dissociation can be controlled by choosing pulses of different shapes and duration. At a particular frequency of the second pulse, the dissociation cross section oscillates with time delay and this oscillation in the cross section can be used as a time-dependent quantum gate.

LOCAL GAUGE INVARIANCE OF RELATIVISTIC QUANTUM MECHANICS AND CLASSICAL RELATIVISTIC FIELDS

We extend our earlier work1 to demonstrate that all free matter fields (Bose as well as Fermi, massive as well as massless), that transform like Φ→TΦ under a local Abelian gauge transformation T=exp(–iβ) with β an arbitrary function of space and time, are governed by field equations that are invariant under such local gauge transformations.

An analytical approach for the nonlinear modified Thomas–Fermi equation to derive the ground-state and dynamic properties of a spherically and cylindrically trapped Bose–Einstein condensate

It has been shown previously that the modified Thomas–Fermi (MTF) equation can be solved analytically by using a higher order iteration method (MTF(p)) for a spherically trapped atomic Bose–Einstein condensate (BEC). The ground-state properties, e.g. chemical potential, peak gas parameter and the ground state density of atoms (except in the surface region), thus obtained can successfully reproduce the results obtained by solving the modified Gross–Pitaevskii (MGP) equation numerically. In this paper, we have extended this analytical method for obtaining the ground-state and dynamical properties of a cylindrically trapped atomic BEC. In this analytical approach, the ground-state density of atoms at the surface of the trap fails to reproduce the correct behaviour due to the neglect of kinetic energy in the MTF equation. We have proposed a model function which when fitted with the analytical wavefunction (from the MTF equation) near the boundaries of the trap can reproduce the correct behaviour of the ground-state density of atoms at the surface region. The kinetic energy and the other energy components thus obtained using the modified analytical method (MTF(p)+model function fitting) can successfully reproduce the results obtained by solving the MGP equation numerically for the 85Rb BEC containing 104 atoms both for spherical and cylindrical traps. The excitation frequency thus obtained for the compressional mode of both spherically and axially symmetric traps is in good agreement with the numerical results. For these calculations, the virial relation is satisfied within the limit ≤10−4.

Control of interference of molecular wavepackets and its dynamics by using delayed phaselocked ultrashort pulses

We have shown by ab-initio calculation that quantum interference between two vibrational wavepackets on the bound A1Σ+ state of NaH molecule can be controlled by controlling the delay time and relative phase between the ultrashort pulses which generate these wavepackets. Quantum interference between the wavepackets is probed by a third pulse which initiates photodissociation of the molecule via repulsive B1II state. Temporal evolution of the photodissociation cross section mimics the dynamics of interfering wavepackets on the bound state. We have shown that the evolution of photodissociation cross section with time can be utilized as time-dependent quantum gate whose nature is a function of the delay time and relative phase between the pulses.

Control of probe response and dispersion in a three level closed Λ system: Interplay between spontaneously generated coherence and dynamically induced coherence

The dispersion and the absorption properties of a closed three-level Λ system with incoherent pumping have been studied when both dynamically induced coherence (DIC) and the spontaneously generated coherence (SGC) play a significant role. We analyze the interplay between the dynamically induced coherence (DIC) and the spontaneously generated coherence (SGC) on the absorption spectrum to induce different nonlinear processes like amplification without population inversion (AWI), electromagnetically induced transparency (EIT) and electromagnetically induced absorption (EIA). By changing the probe field Rabi frequency the response of the system can switch over from one nonlinear process to other and hence the probe field Rabi frequency can be used as a knob for switching different nonlinear responses. By changing the relative phase of two fields the response of the system switches over from EIA to EIT or EIT to AWI which can be used as optical switch. Choosing appropriate value of the relative phase and the probe field Rabi frequency, the dispersion and hence the propagation of the probe pulse can be controlled efficiently. Therefore these parameters can be used as a knob to manipulate light propagation from subluminal to superluminal. Exact analytical expressions for the coherences and populations in the steady state limit have been derived (keeping all orders of system parameters) to generalize the analysis. Any restrictions over the system parameters have been avoided to make it applicable to various atomic and molecular systems.

Control of de-excitation to selected vibrational levels in the ground state of NaH molecule using two broadband ultrashort pulses

We show that the de-excitation to different vibrational levels of the ground state in NaH molecule can be controlled by using two delayed ultrashort pulses (4 fs Gaussian). A vibrational wave packet generated on the excited A1Σ+ state by the first pulse is de-excited back to the ground state by a second pulse after a time delay. The cross-section for de-excitation of the wave packet to different vibrational levels of the ground electronic state can be controlled by controlling the delay time between the two pulses as well as by choosing a pulse duration much shorter than the vibrational period of the molecule, such that the de-excited wave packet remains localized in the Franck–Condon region of a particular vibrational level of the ground state. Hence, the de-excitation to a particular vibrational level can be enhanced by suppressing that in others. In spite of the large bandwidth of the pulse which includes nine vibrational levels of the upper state and five vibrational levels of the ground state, one can selectively de-excite the molecule to any one or two vibrational levels of the ground state by carefully choosing the delay time between the pulses and the pulse duration. We are designing the wave packet in the ground state by two short pulses and selectively distributing the population in one or two levels at various values of the delay time. In light molecules having small vibrational period, this selectivity in de-excitation to one or two vibrational levels in the ground state can be achieved only by using ultrashort (4 fs) pulses in the presence of which the localization of the wave packet in the Franck–Condon region of the vibrational levels are particularly possible. It has been shown that the de-excitation cross-section to a particular vibrational level oscillates with delay between the pulses which can be realized as a time-dependent quantum gate.

Lasing without population inversion in molecules

We have described here the physical basis for lasing without population inversion (LWOPI). This type of amplification is obtained basically by two mechanisms: (i) one is based on atomic interference and (ii) the other is based on Fano-type interference. We have shown here, in H2 molecules, amplification without population inversion is feasible by considering both the mechanisms.