Spontaneous decay controlled inversionless laser in a V-type four level system

By using a semiclassical approach, we obtain 16 coupled optical Bloch equations involving density matrix elements for a V-type four level system with three closely spaced upper levels irradiated by a single mode of the electromagnetic field. The off-diagonal elements of the density matrix ρ_ij are in general complex and arise due to the interference between the probability amplitudes of the levels i and j. Through the complex off-diagonal density matrix elements, we introduce the phase angles between the levels participating in dipole allowed/forbidden transitions. Therefore, the phase angles may be regarded as the outcome of the quantum coherence. Under rotating wave approximation, we use a perturbative approach to solve these Bloch equations analytically. These solutions for density matrix elements are used to obtain a closed form analytical expression for the imaginary part of the polarization and hence the absorptive lineshape. The proper choice of the decay constants induces the necessary coherence responsible for inversionless laser.     

A theoretical analysis on coherent double resonant absorptive lineshape in closely spaced transitions for λ − type five level system

Under Doppler free double resonant condition, an open five level system with three closely spaced upper levels and a pair of closely spaced lower levels, is allowed to interact with two electromagnetic fields. In the domain of semiclassical formulation of atom-field interaction, the optical Bloch equations involving the density matrix elements are constructed. These coupled optical Bloch equations are unsolvable in closed analytical form. We use the perturbation method for getting the approximate analytical solutions to the coupled optical Bloch equations. The absorptive signal lineshape corresponding to pump frequency Ω₁ and signal frequency Ω₂ is obtained. We also obtain the absorptive signal line shape by interchanging the pump and signal (i.e., the pump frequency is Ω₂ and the signal frequency is Ω₁) mutually. The interferences between the probability amplitudes for different energy levels involving the dipole allowed and the dipole forbidden transitions give rise to the field dependent and field independent quantum coherence respectively. With the suitable manipulation of the coherence between the two lower levels, the signal lineshapes for on-resonance and off-resonance pump positions are explored in a great detail. The off-resonance pump leads to the two-photon absorption and hence the signature of the nonlinear resonances. On the other hand, the on-resonance pump positions lead to the Rabi splitting. The shifts of the resonance peak positions are explored as a function of pump intensity and the level spacings of the closely spaced levels.     

Effects of spontaneous decay on absorptive lineshape in closely spaced transitions of an open four level system

A semi classical treatment of atom field interaction is adopted under Doppler free condition, for an open four level system with three closely spaced upper levels. The field induced polarization in closed analytical form is used in order to examine the absorption lineshape. Through the off-diagonal density matrix elements, the introduction of phase angles between the levels participating in dipole allowed / forbidden transitions are automatic. By the proper control of ground level decay and field independent coherence, we obtain inversionless gain.     

On a physical implementation of logical operators NOT and CNOT in a two-qubit quantum computer controlled by ultrashort optical pulses

It is shown that it is preferable to perform quantum computations on a system of two-level atoms with metastable states using optical dipole transitions that occur under the effect of ultrashort light pulses. It is suggested to measure the quantum information that is passed to qubits using Bloch, rather than pure, quantum states of two-level atoms. Moreover, the inversion of atoms can be used as the measure of quantum information. In order to describe the logical operators NOT and CNOT in the system of interacting two-level atoms (qubits), modified optical equations for the Bloch vectors of individual qubits are derived. These equations are solved in combination with field equations, without using the slowly varying amplitude approximation, for a small two-qubit system in the field of ultrashort intense optical pulses of arbitrary shape. A numerical analysis of the solution shows that it is possible to control the recording of information on individual qubits in a small quantum system of a dimension much smaller than the length of the optical wave by smoothly varying the irradiation conditions of qubits.     

Switching from positive to negative absorption with electromagnetically induced transparency in circuit quantum electrodynamics

We present a theoretical study of electromagnetically induced transparency(EIT) in a superconducting quantum circuit with a tunable V-shaped energy spectrum derived from two superconducting Josephson charge qubits coupled with each other through a superconducting quantum interference device. Using the density matrix formalism and the steady-state approximation, we obtain the analytical expressions of the first-order matrix element associated with the absorption and dispersion of the probe field for two different V-type schemes. Our results show that, for this superconducting quantum system, it is possible to realize a remarkable phenomenon that dynamic conversion between EIT and EIT with amplification without population inversion. Such a unique optical feature has potential applications in quantum optical devices and quantum information processing.     

Dispersive optical bistability in a nonideal Fabry-Pérot cavity

A stability analysis is performed for optical bistability in a Fabry-Pérot cavity with mirrors of arbitrary transmission coefficient. The mixed absorptive and dispersive régime is covered. In order to describe the system we use the Maxwell0Bloch equations formulated in terms of slowly varying envelopes. Standing-wave effects are completely taken into account by refraining from a truncation of the harmonic expansions for the polarization and the inversion density. We represent the solutions of the linearized Bloch hierarchy in terms of Chebyshev polynomials depending on the stationary electric field envelopes. In this way, we reduce the stability problem to a four-dimensional set of linear differential equations. Together with a couple of boundary conditions these equations govern the spatial behaviour of the deviations of the forward and the backward electric field envelopes. Our final stability problem becomes much simpler in the uniform-field limit and in the adiabatic limit. If we choose the stationary backward electric field equal to zero we recover results that were derived earlier for the case of a ring cavity.     

Two-photon optical bistability of polar molecules inserted in a solid matrix: Phonon effects

Single-beam two-photon optical bistability in a Fabry-Perot cavity filled with molecules which change permanent dipole moment upon electronic excitation is analysed under the mean-field and plane-wave approximations. One-photon resonances are discarded. These molecules are assumed to be in a solid matrix. Phonon effects are then taken into account. The Bloch equations of the system are further coupled by a term that is dependent on the electron-phonon interaction, leading to shifts in the switching thresholds which modify the optical bistability character. Such a term becomes irrelevant when the difference between the dipole moments is much greater than the transition dipole moment.     

Dipole matrix elements of semiconductor intersubband quantum structures

A method for determining the dipole matrix element for an intersubband optical transition in multi-layered semiconductor quantum heterostructures is presented. The single-band effective-mass Schrödinger equation is solved by employing the argument principle method (APM) to extract the bound (B) and quasibound (QB) eigenenergies of the quantum heterostructure. The major types of optical transitions involving bound and QB states are defined and the corresponding dipole matrix elements are calculated for each type. The method presented incorporates the energy-dependent effective mass of electrons arising from conduction-band nonparabolicity. The performance and the accuracy of the method are evaluated for an asymmetric Fabry–Perot electron wave interference filter. The physical dimensions of the filter are varied to show their effect on the dipole matrix elements. Results with and without nonparabolic effects are presented and compared. Dipole matrix elements are also calculated for the filter with an applied electric field bias. In this case the eigenstate wavefunctions can be expanded as linear combinations of Airy and complementary Airy functions. In addition, results from the present method are compared to a Kronig–Penney and a multi-band model. The dipole matrix element values calculated by the present method are shown to be in excellent agreement with the values obtained from these models. Further, the present model is numerically efficient and easily implemented.     

四能级原子系统中电磁感应吸收的相位控制

在以三个电偶极跃迁构成简并N型四能级系统中,利用密度矩阵方程计算了介质对探测场的吸收,研究了激光场拉比相位对吸收的影响.结果表明:介质对探测场的吸收和放大取决于控制场和信号场的拉比相位,且吸收和放大随控制场、信号场的拉比相位改变而作周期性变化,周期为2π;而探测场的拉比相位变化对吸收没有影响.同时,控制场、信号场拉比相位对吸收的影响是相同的,而且拉比相位主要影响原子相干,对原子布居影响不大.     

Coherence control for photonic logic gates via Y-configuration double-control quantum interferences

Destructive and constructive quantum interferences exhibited in a four-level Y-configuration double-control atomic system are suggested. It is shown that the probe transition (driven by the probe field) can be manipulated by the quantum interferences between two control transitions (driven by the control fields) of the four-level system. The atomic vapor is opaque (or transparent) to the probe field if the destructive (or constructive) quantum interference between the control transitions emerges. The optically sensitive responses due to double-control quantum interferences can be utilized to realize some quantum optical and photonic devices such as the logic-gate devices, e.g., the NOT, OR, NOR and EXNOR gates.     

Electromagnetically induced transparency and electromagnetically induced absorption in Y-type system

The propagation of a probe field through a four-level Y-type atomic system is described in the presence of two additional coherent radiation fields, namely, the control field and the coupling field. An expression for the probe response is derived analytically from the optical Bloch equations under steady state condition to study the absorptive properties of the system under probe field propagation through an ensemble of stationary atoms as well as in a Doppler broadened atomic vapor medium. The most striking result is the conversion of electromagnetically induced transparency(EIT) into electromagnetically induced absorption(EIA) as we start switching from weak probe regime to strong probe regime. The dependence of this conversion on residual Doppler averaging due to wavelength mismatch is also shown by choosing the coupling transition as a Rydberg transition.     

Absorptive and dispersive optical profiles in fluctuating environments: A stochastic model

In this study, we determined the absorptive and dispersive optical profiles of a molecular system coupled with a thermal bath. Solvent effects were explicitly considered by modelling the non-radiative interaction with the solute as a random variable. The optical stochastical Bloch equations (OSBE) were solved using a time-ordered cumulant expansion with white noise as a correlation function. We found a solution for the Fourier component of coherence at the third order of perturbation for the nonlinear Four-wave mixing signal and produced analytical expressions for the optical responses of the system. Finally, we examined the behaviour of these properties with respect to the noise parameter, frequency detuning of the dynamic perturbation, and relaxation times.     

Kerr non-linearity and four-wave mixing in a double-cascade type four-level system of multiple quantum wells

We study the non-linear optical response in multiple quantum wells structure with a double-cascade type four-level configuration based on excitons and biexcitons transitions. By analysing the Kerr non-linear effects, we obtain the slow, mutually matched group velocities and giant Kerr non-linearity of probe and signal fields. While when the signal (or probe) field is removed, the non-linear optical phenomenon four-wave mixing (FWM) originating from quantum interference is demonstrated. The FWM efficiency of the system study is about 50%. Such a semiconductor system is much more practical than its atomic counterpart because of its flexible design and the controllable interference strength.     

Tunable ultra-fast carrier–light field dynamics of quantum dots

A theory of ultra-fast carrier–light field dynamics of quantum dots is presented. The carrier–light field dynamics is described by Maxwell–Bloch equations. A calculation of the dipole matrix elements requires the determination of the electronic wave functions taking into account their dependence on the degeneracy of the carrier states. The ultra-fast carrier–light field dynamics depends strongly on the external applied electric field. PACS 42.55.Px; 42.60.Rn; 74.78.Fk     

Vector solitons in semiconductor quantum dots

A theory of an optical vector soliton of self-induced transparency in an ensemble of semiconductor quantum dots is considered. By using the perturbative reduction method, the system of the Maxwell–Liouville equations is reduced to the two-component coupled nonlinear Schrödinger equations. It is shown that a distribution of transition dipole moments of the quantum dots and phase modulation changes significantly the pulse parameters. The shape of the optical two-component vector soliton with the sum and difference of the frequencies in the region of the carrier frequency is presented. The vector soliton can be reduced to the breather solution of self-induced transparency with a different profile. Explicit analytical expressions in the presence of single-excitonic and biexcitonic transitions for the optical vector soliton are obtained with realistic parameters which can be reached in current experiments.     

Quantum interference and population swapping in single quantum dots with V-type three-level

The quantum interference and Rabi oscillation of a V-type three-level system with two orthogonal sub-states in an elongated semiconductor quantum dot are discussed theoretically with optical Bloch equations when the system is driven by pulse-pair. Numerical calculations from the optical Bloch equations reveal that the quantum interference in the system is enhanced with the increasing of the energy decay or splitting. Furthermore, the populations swapping in two orthogonal sub-states can be realized though the direct transition is prohibited.     

Intraband Dynamics and Terahertz Emission in Biased GaAs/In0.53Ga0.47As Semiconductor Superlattices

Using an excitonic basis, we investigate the intraband polarization, opticalabsorption spectra, and terahertz emission of semiconductor superlattice withthe density matrix theory. The excitonic Bloch oscillation is driven by the dcand ac electric fields. The slow variation in the intraband polarizationdepends on the ac electric field frequency. The intraband polarizationincreases when the ac electric field frequency is below the Bloch frequency.When the ac electric field frequency is above the Bloch frequency, theintraband polarization downwards and its intensity decreases. The satellitestructures in the optical absorption spectra are presented. Due to excitonicdynamic localization, the emission lines of terahertz shift in different acelectric field and dc electric field.     

Metric-Space Approach for Distinguishing Quantum Phase Transitions in Spin-Imbalanced Systems

Metric spaces are characterized by distances between pairs of elements. Systems that are physically similar are expected to present smaller distances (between their densities, wave functions, and potentials) than systems that present different physical behaviors. For this reason, metric spaces are good candidates for probing quantum phase transitions, since they could identify regimes of distinct phases. Here, we apply metric space analysis to explore the transitions between the several phases in spin-imbalanced systems. In particular, we investigate the so-called FFLO (Fulde-Ferrel-Larkin-Ovchinnikov) phase, which is an intriguing phenomenon in which superconductivity and magnetism coexist in the same material. This is expected to appear for example in attractive fermionic systems with spin-imbalanced populations, due to the internal polarization produced by the imbalance. The transition between FFLO phase (superconducting phase) and the normal phase (non-superconducting) and their boundaries have been subject of discussion in recent years. We consider the Hubbard model in the attractive regime for which density matrix renormalization group calculations allow us to obtain the exact density function of the system. We then analyze the exact density distances as a function of the polarization. We find that our distances display signatures of the distinct quantum phases in spin-imbalanced fermionic systems: with respect to a central reference polarization, systems without FFLO present a very symmetric behavior, while systems with phase transitions are asymmetric.