Dynamic Stark Splitting Research Articles

Two-photon resonances, ac Stark splittings, and shifts of the resonance peaks in Doppler free absorptive lineshapes of a double-lambda type four level system

Under Doppler free condition and by using semiclassical approach, a double-lambda type four-level system coupled to two electromagnetic fields are investigated. The coupled optical Bloch equations involving the density matrix elements in steady state are solved numerically to investigate the signal lineshapes as the function of signal detuning and pump Rabi-frequencies. The on-resonant pump leads to dynamic Stark splitting. The dent in the absorption lineshape is exhibited for off-resonant pump and is a signature of two-photon resonances. The appearance of extra absorption and emission peaks in the computed lineshapes are attributed by the nonlinear polarizations and hence the spontaneously generated coherences.

Optical resonance near the edge of a photonic band gap (PBG): turning the effects of a PBG on/off using a resonant driving field

ABSTRACTWe studied the effects of a coherent monochromatic resonant laser field driving the transition of a two-level atom embedded in a photonic band gap (PBG) material on the emission dynamics of the atom. When the transition frequency of the atom lies outside a PBG and sufficiently far from the band edge that the emission dynamics of the atom is not normally affected by the gap, the dynamic stark splitting of the upper level of the atom into two dressed states by a sufficiently strong resonant driving field can bring the lower dressed state close enough to the band edge or even inside the gap so as to be affected by the gap, providing a switchable means of extending the novel effects of atom–photon interaction near the edge of a PBG for atomic transitions outside the gap and far from the band edge. The net effect is as if a sufficiently strong resonant field driving a transition of an atom embedded in a PBG actively shifts the PBG close enough to the transition so that the gap affects the emission dynamics associated with the transition.

Noise property of a four-level system in vee + ladder configuration

We present the results of a theoretical study of the output amplitude noises of a four-level atomic system in vee + ladder configuration. The difference and connection of electromagnetically induced transparency and Autler–Townes splitting effects are investigated theoretically. The output amplitude noise of the probe field of two effects were compared, the quantum properties of the input field of the thin medium and the thick medium under Autler–Townes splitting or electromagnetically induced transparency (EIT) condition are maintained, the higher fidelity is obtained in the storage of the thick medium under the condition of EIT in non-classical states. The noise characteristics of the squeezed vacuum field after four-level coherent medium are studied; the noise of the output field is lowest when the detection light is far away from detuning. The double split of EIT window was made by the dynamic Stark splitting on the ground state of control field, the quantum properties of the input field in the strong-control field and strong-coupling field were maintained. The output noise spectrum is divided with the increase in the field strength, the maximum output squeezing is far away from the resonance.

Controllable double tunneling induced transparency and solitons formation in a quantum dot molecule

We consider the coupling effect between interdot tunneling coupling and external optical control field to study the linear optical property and the formation of temporal optical solitons in a quantum dot molecules system, analytically. The results show that the double tunneling induced transparency (TIT) windows are appeared in the absorption curve of probe field because of the formation of dynamic Stark splitting and quantum destructive interference effect from the two upper levels. Interestingly, the width of the TIT window becomes wider with the increasing intensity of the optical control field. We also find that the Kerr nonlinear effect of the probe field can be modulated effectively through coherent control both the control field and the interdot tunneling coupling in this system. Meanwhile, we demonstrate that the formation of dark or bright solitons can be practical regulated by varying the intensity of the optical control field.

Nuclear-spin-dependent coherent population trapping of single nitrogen-vacancy centers in diamond

Coherent population trapping (CPT) provides a highly sensitive means for probing the energy level structure of an atomic system. For a nitrogen vacancy center in diamond, the CPT offers an alternative to the standard optically-detected magnetic resonance method for measuring the hyperfine structure of the electronic ground states. We show that the nuclear spin dependent CPT measures directly the hyperfine splitting of these states due to the 14N nuclear spin. The CPT spectral response obtained in the presence of a strong microwave field, resonant or nearly resonant with a ground state spin transition, maps out the dynamic Stark splitting induced by the coherent spin excitation.

Manipulation of squeezed state in electromagnetically induced transparency system via dynamic Stark effect

We calculate the delay time and noise spectrum of a squeezed state throughout an electromagnetically induced transparency medium with dynamic Stark splitting. It is shown that the noise spectrum splits into two parts with the same delay time, so that the delayed squeezing can survive well in two channels. Furthermore, we show that the two squeezing channels as well as the delay time can be manipulated via one-photon detuning and detection frequency such that the quantum state with high delay time and squeezing can be well preserved. This avoids the influence of large noise from laser near zero detection frequency.

ChemInform Abstract: Observation of Dynamic Stark Splitting in Infrared-Infrared Double Resonance in Methyl Fluoride.

Abstract Dynamic Stark splitting has been observed by scanning the Q P (5, 3) transition in the 2 ν 3 - ν 3 band in 13 CH 3 F with a CO 2 -laser based infrared microwave sideband generator while pumping the Q R (4, 3) transition in the ν 3 band with a second CO 2 laser. Similar splitting has been observed in the Q Q (12, 9) and Q R (12, 9) transitions in the 2 ν 3 - ν 3 band of 12 CH 3 F while pumping the Q R (11, 9) transition in the ν 3 band. The lineshapes of these and other double resonance effects have been fit to high accuracy by means of a computer program that computes the spectrum by solving the density matrix equations for a three-level system including summation over the spatially degenerate states and numerical integration over the velocity. The effects of contributions from collisional energy transfer, frequency modulation of the lasers, and misalignment of the laser beams have been calculated and are discussed. Difficulties that must be overcome in order to use these experiments for determination of energy transfer rates are described.

Inhibition of two-photon absorption in a three-level system with a pair of bichromatic fields

We study two-photon absorption in a three-level ladder atomic system driven by a pair of bichromatic fields of equal frequency differences. The high-frequency component of one bichromatic field and the low-frequency component of the other are on two-photon resonance. The transition probability is calculated by employing the method of harmonic expansion and matrix inversion. Unexpectedly, when the sums of the phases of the different pairs of field components on the two-photon resonance are equal to each other, two-photon absorption is dramatically suppressed and the atomic system becomes transparent against two-photon absorption. Physically, due to dynamical Stark splitting, the two-photon transitions induced by the different pairs of field components experience different dressed states with phase difference of $\ensuremath{\pi}$. As a result, destructive interference occurs between the two pathways and leads to the inhibition of two-photon absorption.

The other side of quantum jumps

Abstract An ion, or atom, confined in a ‘trap’ and laser-irradiated on its resonance line generates a quasi-continuous flow of scattered light, and makes the line split or shifted. When the ion is probe-laser excited, on a neighbouring dipole-forbidden line to a metastable state, the flow subsides. Also, the shift or dynamic Stark splitting of the resonance and of the dipole-forbidden line vanishes. De-excitation of the ion requires the probe laser to be re-tuned to the unshifted resonance. Cyclic scanning of this laser shows a mean frequency offset of the on-off jumps from the off-on jumps. This random hysteresis may cool or heat the ion, and lock an ensemble in the metastable state.

The other side of quantum jumps

An ion, or atom, confined in a ‘trap’ and laser-irradiated on its resonance line generates a quasi-continuous flow of scattered light, and makes the line split or shifted. When the ion is probe-laser excited, on a neighbouring dipole-forbidden line to a metastable state, the flow subsides. Also, the shift or dynamic Stark splitting of the resonance and of the dipole-forbidden line vanishes. De-excitation of the ion requires the probe laser to be re-tuned to the unshifted resonance. Cyclic scanning of this laser shows a mean frequency offset of the on-off jumps from the off-on jumps. This random hysteresis may cool or heat the ion, and lock an ensemble in the metastable state.

Polariton analysis of a four-level atom strongly coupled to a cavity mode

We present a complete analytical solution for a single four-level atom strongly coupled to a cavity field mode and driven by external coherent laser fields. The four-level atomic system consists of a three-level subsystem in an electromagnetically induced transparency configuration, plus an additional atomic level; this system has been predicted to exhibit a photon blockade effect. The solution is presented in terms of polaritons. An effective Hamiltonian obtained by this procedure is analyzed from the viewpoint of an effective two-level system, and the dynamic Stark splitting of dressed states is discussed. The fluorescence spectrum of light exiting the cavity mode is analyzed and relevant transitions identified.

Direct observation of the excitonic ac Stark splitting in a quantum well

Ultrafast pump-probe measurements evidence the dynamical Stark splitting in the exciton absorption spectrum of a single semiconductor quantum well. The intensity of the Stark sidebands in the spectrum is comparable to the linear absorption and their separation scales as the pump field amplitude. In the time domain the Rabi oscillations are observed. The semiconductor Bloch equations solved in the Hartree-Fock approximation demonstrate that the coherent exciton-light coupling dominates over the many-body dephasing.

Coherence versus Coulomb Scattering in Resonantly Excited Quantum Wells

The role of Coulomb scattering is studied in the coherent transients of strongly driven exciton resonances in semiconductor quantum wells. Coulomb scattering is treated within the second Born approximation and the light-induced dressing of the electron–hole gas is consistently included. The light dressing is found to decrease the Coulomb collision efficiency and therefore the field-driven dynamics is close to the Hartree-Fock case. Indeed, Coulomb relaxation and dephasing are not strong enough to prevent a dynamical Stark splitting in the pump–probe absorption spectra.

Strongly driven exciton resonances in quantum wells: light-induced dressing versus coulomb scattering

The nonequilibrium dynamics of a two-dimensional electron-hole gas is studied in the regime of strong and resonant pumping of the exciton resonance. The Coulomb collision rates are consistently determined by taking into account the light-induced coherence of the two-band system that leads to a dressing of the carrier spectral functions. The light dressing dramatically reduces the Coulomb scattering efficiency. Results are presented for Rabi oscillations in the time domain and dynamical Stark splitting in the pump-probe absorption spectra.

Observation of the dynamic Stark effect on electromagnetically induced transparency

Using electron-spin-resonance transitions within the nitrogen-vacancy center in diamond, we have obtained a sharp electromagnetically induced transparency (EIT) feature when the coupling and probing fields satisfy a two-photon resonance condition. In this paper it is shown that by the application of an additional driving field the sharp EIT feature can be split into a doublet or a triplet depending on the experimental configuration. The results are interpreted in terms of dynamic Stark splitting of the EIT feature, and the spectra are shown to be related to Autler-Townes and Mollow spectra.

Pump-probe spectra and nuclear dynamics for a dissipative molecular system in a strong laser field: predissociation dynamics

The predissociation dynamics of a molecular system under a strong laser field in the condensed phase is investigated by direct numerical integration of the multi-state quantum Fokker-Planck equation. Numerical calculations of probe absorption spectra driven by a strong pump pulse are presented, and discussed. The results show dynamical Stark splitting, but, in contrast to the Bloch equations which contain an infinite-temperature dephasing, we find that at finite temperatures their peaks have different heights even when the pump pulse is on resonance. Furthermore we observe the effect of the diabatic coupling between excited and dissociative states as the peaks on the spectra.

A strongly driven two-level atom revisited: Bloch - Siegert shift versus dynamic Stark splitting

We calculate a probe response of a homogeneously broadened two-level transition in the presence of a strong pump. The derivation is carried out for a generalized interaction Hamiltonian, which gives a uniform account of both the Bloch - Siegert shift and dynamic Stark splitting. It is shown that the Bloch - Siegert shift can be viewed as an extreme situation of the dynamic Stark splitting, commonly known as light shift in the literature. Finally using a perturbative approach an analytical expression for the Bloch - Siegert shift is obtained, which is compared with the previous results.

Gaussian–Markovian quantum Fokker–Planck approach to nonlinear spectroscopy of a displaced Morse potentials system: Dissociation, predissociation, and optical Stark effects

Quantum coherence and its dephasing by coupling to a dissipative environment play an important role in time-resolved nonlinear optical response as well as nonadiabatic transitions in the condensed phase. We have discussed nonlinear optical processes on a multi-state one-dimensional system with Morse potential surfaces in a dissipative environment. This was based on a numerical study using the multi-state quantum Fokker–Planck equation for a colored Gaussian–Markovian noise bath, which was expressed as a hierarchy of kinetic equations. This equation can treat strong system-bath interactions at a low temperature heat bath, where quantum effects play a major role. The approach applies to linear absorption measurements as well as four-wave mixing including pump-probe spectroscopy. Laser induced photodissociation and predissociation have been studied for the potential surfaces of Cs2. We have calculated nuclear wave packets in Wigner representation and their monitoring by femtosecond pump-probe spectroscopy for various displacements of potentials and heat-bath parameters. Numerical calculations of probe absorption spectra for strong pump pulse are also presented and discussed. The results show dynamical Stark splitting, but, in contrast to the Bloch equations which contain an infinite-temperature dephasing, we find that at finite temperature their peaks have different heights even when the pump pulse is on resonance.

A strongly driven two-level transition in a solid state: Small inhomogeneous broadening

The non-linear behavior of a two-level transition driven by a strong field plays an important role in the solid state laser spectroscopy, where the transitions are normally inhomogeneously broadened. In this paper, we study phenomena associated with the lesser-known situation in the solid state where the transition between two levels has little inhomogeneous broadening. The two-level transition studied involves hyperfine levels of nitrogen-vacancy color centers in diamond and is detected by an optical-RF double resonance technique. Many interesting effects will be described, including dynamic Stark splitting, Autler-Townes splitting, gain without inversion and multiphoton transitions.

Optical Stark Spectroscopy of a Brownian Oscillator in Intense Fields

The optical Stark effect of a two-level system coupled to a Brownian oscillator (i.e. a harmonic mode which in turn is coupled to a heat bath) is studied using equations of motion for a reduced density matrix. These equations, derived using path integral techniques, can be used to study the combined effects of strong fields and dephasing processes at finite temperature, and interpolate continuously from the coherent to the overdamped limits where they reduce to the stochastic Gaussian-Markovian equation. Numerical calculations of probe absorption spectra for various pump intensities are presented, and show dynamical Stark splitting. In contrast to the Bloch equations which contain an infinite-temperature dephasing, we find that at finite temperature, the Stark peaks may have different heights even when the pump pulse is on resonance.