Collisional Dephasing Research Articles

Water vapor in hydrogen flames measured by time-resolved collisional dephasing of the pure-rotational N2 CARS signal

We present a novel diagnostic technique to probe water vapor (H2O) concentration in hydrogen (H2) combustion environments via the time-resolved measurement of the collisional dephasing of the pure-rotational coherent anti-Stokes Raman scattering (CARS) signal of nitrogen (N2). The rotational Raman coherence of the N2 molecules, induced by the interaction with the pump and Stokes laser fields, dephases on a timescale of hundreds of picoseconds (ps), mostly due to inelastic collisions with other molecules in atmospheric flames. In the spatial region of H2 flames where H2O is present in appreciable amount, it introduces a faster dephasing of the N2 coherence than the other major combustion species do: we use time-resolved femtosecond/picosecond (fs/ps) CARS to deduce the H2O mole fraction from the dephasing effect of its inelastic collisions with N2. The proof-of-principle is demonstrated in a laminar H2/air diffusion flame, performing sequential measurements of the collisional dephasing of the N2 CARS signal up to 360 ps. We measure the temperature and the relative O2/N2 and H2/N2 concentrations at a short probe delay, and input the results in the time-domain model to extract the H2O mole fraction from the signal decay, thus measuring the whole scalar flow fields across the flame front. We furthermore present single-shot simultaneous thermometry and absolute concentration measurements in the turbulent TU Darmstadt/DLR Stuttgart canonical ‘H3 flame’ performed by dual-probe CARS measurements obtained with a polarization separation approach. This allows us to probe the molecular coherence simultaneously at ∼20 and ∼250 ps on the basis of a single-laser-shot, and record the resulting signals in two distinct detection channels of our unique polarization-sensitive coherent imaging spectrometer. The proposed technique allows for measuring the absolute concentrations of all the major species of H2 flames, thus providing a full characterization of the flow composition, as well as of the temperature field.

Semiclassical control theory of coherent anti-Stokes Raman scattering maximizing vibrational coherence for remote detection

A semiclassical theory that describes the generation of a coherent anti-Stokes Raman scattering (CARS) signal is presented that maximizes vibrational coherence in a mode predetermined by the pump, the Stokes, and the probe chirped pulse trains and takes into account the field propagation effects in a cloud of molecules. The buildup of the anti-Stokes signal, which may be used as a molecular signature in the backward CARS signal, is demonstrated numerically. The theory is based on the solution of the coupled Maxwell's and Liouville--von Neumann equations and focuses on the quantum effects induced in the target molecules by the control pulse trains. A deep convolutional neural network technique is implemented to evaluate time-dependent phase characteristics of the control fields. The effect of decoherence induced by spontaneous decay and collisional dephasing is examined.

Oxygen rotational Raman linewidth determination considering nonmonoexponential decoherence behavior

AbstractThe rotational Raman linewidth is a vital empirical parameter in determining temperature and concentration in combustion environments from pure rotational anti‐Stokes Raman spectroscopy (RCARS). The Raman linewidth is regularly determined from the coherence dephasing time constant on a picosecond time scale. Oxy‐fuel combustion processes cannot be studied applying the well‐described nitrogen evaluation but are typically based on oxygen evaluation. Therefore, the dephasing behavior of the rotational Raman coherences of oxygen was studied by picosecond time resolved RCARS. In opposite to nitrogen, the dephasing in oxygen shows distinct quantum beating rendering monoexponential fitting functions unsuited for the evaluation. Therefore, collisional dephasing time constants were obtained from a coherent beating model function. The acquired Raman linewidths show comparable trends with increasing temperature and rotational quantum number as nitrogen but differ from O2‐linewidths used for evaluations up to now. Therefore, an improvement of temperature and concentration evaluations based on oxygen RCARS measurements by application of the S‐branch linewidth can be expected.

Single-mode scannable nanosecond Ti:sapphire laser for high-resolution two-photon absorption laser-induced fluorescence (TALIF)

A pulsed Ti:sapphire laser has been developed so as to operate over a wide range of frequencies, even far from the optimum wavelength (790 nm), as a narrow-band light source for TALIF experiments on O, Cl, N and H. The coupling of the optical cavity, both to its injection seeder and to the laser output beam, relies on a reflecting plate, which makes it fundamentally easier to control the coupling coefficient over a wider spectral range than with an ordinary transmission coupler. Two intra-cavity prisms are used to bring the green pumping light longitudinally coincident with the cavity axis, inside the Ti:sapphire crystal. Seeding by a CW Ti:sapphire laser has made it possible to obtain single-mode emission over the whole range of tunability, thanks to the spectral selection of the prisms and to a specifically developed digital/analog controller. Experiments carried out with the system on oxygen atoms inside an oxygen plasma show that the experimental bandwidth is limited essentially by the collisional dephasing rate and the finite pulse duration.

A model study of assisted adiabatic transfer of population in the presence of collisional dephasing.

Previous studies have demonstrated that when experimental conditions generate non-adiabatic dynamics that prevents highly efficient population transfer between states of an isolated system by stimulated Raman adiabatic passage (STIRAP), the addition of an auxiliary counter-diabatic field (CDF) can restore most or all of that efficiency. This paper examines whether that strategy is also successful in a non-isolated system in which the energies of the states fluctuate, e.g., when a solute is subject to collisions with solvent. We study population transfer in two model systems: (i) the three-state system used by Demirplak and Rice [J. Chem. Phys. 116, 8028 (2002)] and (ii) a four-state system, derived from the simulation studies of Demirplak and Rice [J. Chem. Phys. 125, 194517 (2006)], that mimics HCl in liquid Ar. Simulation studies of the vibrational manifold of HCl in dense fluid Ar show that the collision induced vibrational energy level fluctuations have asymmetric distributions. Representations of these asymmetric energy level fluctuation distributions are used in both models (i) and (ii). We identify three sources of degradation of the efficiency of STIRAP generated selective population transfer in model (ii): too small pulse areas of the laser fields, unwanted interference arising from use of strong fields, and the vibrational detuning. For both models (i) and (ii), our examination of the efficiency of STIRAP + CDF population transfer under the influence of the asymmetric distribution of the vibrational energy fluctuations shows that there is a range of field strengths and pulse durations under which STIRAP + CDF control of population transfer has greater efficiency than does STIRAP generated population transfer.

Remote atmospheric optical magnetometry

In this paper, an analysis of a remote atmospheric magnetometry concept is considered, using molecular oxygen as the paramagnetic species. The objective is to use this mechanism for the remote detection of underwater and underground objects. Kerr self-focusing is used to bring a polarized, high-intensity, laser pulse to focus at a remote detection site where the laser pulse induces a ringing in the oxygen magnetization current. This current creates a co-propagating electromagnetic field behind the laser pulse, i.e., the wakefield, which has a rotated polarization that depends on the background magnetic field. The detection signature for underwater and underground objects is the change in the wakefield polarization between different measurement locations. The coupled Maxwell-density matrix equations are used to describe the oxygen magnetization in the presence of an intense laser pulse and ambient magnetic field. The magnetic dipole transition line that is considered is the b1Σg+−X3Σg− transition band of oxygen near 762 nm. The major challenges are the collisional dephasing of the atmospheric oxygen transitions and the strength of the effective magnetic dipole interaction.

Coherence dynamics of a two-mode Bose-Einstein condensate coupled with the environment

We investigate the coherence dynamics of a two-mode Bose-Einstein condensate coupled with the environment in the mean-field approximation. We give an analytical result of the time-average coherence in the absence of system-environment coupling, and find that the time-average coherence attains its maximum value at the critical point which corresponds to the boundary between the self-trapping regime and the Josephson oscillation regime. The effect of noise on dynamical coherence is also considered by analyzing the couplings of the condensate to the environment. With the first kind of coupling, the coherence finally stabilizes at a fixed value. Meanwhile, we show that the presence of the noise can even enhance the coherence for some particular interaction. With the second kind of coupling as collisional dephasing, the noise leads a sudden transition of the coherence which then subjects to an exponential decay.

Split-probe hybrid femtosecond/picosecond rotational CARS for time-domain measurement of S-branch Raman linewidths within a single laser shot

We introduce a multiplex technique for the single-laser-shot determination of S-branch Raman linewidths with high accuracy and precision by implementing hybrid femtosecond (fs)/picosecond (ps) rotational coherent anti-Stokes Raman spectroscopy (CARS) with multiple spatially and temporally separated probe beams derived from a single laser pulse. The probe beams scatter from the rotational coherence driven by the fs pump and Stokes pulses at four different probe pulse delay times spanning 360 ps, thereby mapping collisional coherence dephasing in time for the populated rotational levels. The probe beams scatter at different folded BOXCARS angles, yielding spatially separated CARS signals which are collected simultaneously on the charge coupled device camera. The technique yields a single-shot standard deviation (1σ) of less than 3.5% in the determination of Raman linewidths and the average linewidth values obtained for N(2) are within 1% of those previously reported. The presented technique opens the possibility for correcting CARS spectra for time-varying collisional environments in operando.

Fisher information under decoherence in Bloch representation

The dynamics of two variants of quantum Fisher information under decoherence is investigated from a geometrical point of view. We first derive the explicit formulas of these two quantities for a single qubit in terms of the Bloch vector. Moreover, we obtain analytical results for them under three different decoherence channels, which are expressed as affine transformation matrices. Using the hierarchy equation method, we numerically study the dynamics of both sets of information in a dissipative model and compare the numerical results with the analytical ones obtained by applying the rotating-wave approximation. We further express the two information quantities in terms of the Bloch vector for a qudit by expanding the density matrix and Hermitian operators in a common set of generators of the Lie algebra $\text{su}(d)$. By calculating the dynamical quantum Fisher information, we find that the collisional dephasing significantly diminishes the precision of the phase parameter with the Ramsey interferometry.

Impact of decoherence on internal state cooling using optical frequency combs

We discuss femtosecond Raman type techniques to control molecular vibrations, which can be implemented for internal state cooling from Feshbach states with the use of optical frequency combs with and without modulation. The technique makes use of multiple two-photon resonances induced by optical frequencies present in the comb. It provides us with a useful tool to study the details of molecular dynamics at ultracold temperatures. In our theoretical model we take into account decoherence in the form of spontaneous emission and collisional dephasing in order to ascertain an accurate model of the population transfer in the three-level system. We analyze the effects of odd and even chirps of the optical frequency comb in the form of sine and cosine functions on the population transfer. We compare the effects of these chirps to the results attained with the standard optical frequency comb to see if they increase the population transfer to the final deeply bound state in the presence of decoherence. We also analyze the inherent phase relation that takes place owing to collisional dephasing between molecules in each of the states. This ability to control the rovibrational states of a molecule with an optical frequency comb enables us to create a deeply bound ultracold polar molecules from the Feshbach state.

Reflectivity and transmissivity of a cavity coupled to two-level systems: Coherence properties and the influence of phase decay

We consider $N$ identical two-level systems coupled to a cavity, which is coherently driven by an external field. In the limit of small excitation, the reflection and transmission coefficients for both fields and intensities are calculated analytically. In addition, the frequency content of the cavity field and hence also the emission spectrum of the cavity are determined. A discussion is presented regarding how, in particular, individual collisional dephasing and common energy-level fluctuations prevent the cavity field from being in a coherent state, which in turn affects the outgoing fields.

Communication: Time-domain measurement of high-pressure N2 and O2 self-broadened linewidths using hybrid femtosecond/picosecond coherent anti-Stokes Raman scattering

The direct measurement of self-broadened linewidths using the time decay of pure-rotational hybrid femtosecond/picosecond coherent anti-Stokes Raman scattering (fs/ps RCARS) signals is demonstrated in gas-phase N(2) and O(2) from 1-20 atm. Using fs pump and Stokes pulses and a spectrally narrowed ps probe pulse, collisional dephasing rates with time constants as short as 2.5 ps are captured with high accuracy for individual rotational transitions. S-branch linewidths of N(2) and O(2) from ~0.06 to 2.2 cm(-1) and the line separation of O(2) triplet states are obtained from the measured dephasing rates and compared with high-resolution, frequency-domain measurements and S-branch approximations using the modified exponential gap model. The accuracy of the current measurements suggests that the fs/ps RCARS approach is well suited for tracking the collisional dynamics of gas-phase mixtures over a wide range of pressures.

Decoherence of high-ℓ Rydberg wave packets

Quantum revivals in very-high-n (n ∼ 300) high-ℓ Rydberg wave packets generated from parent np states are used to examine decoherence induced by the application of ‘coloured’ noise from a random pulse generator and by collisions. In the absence of external perturbations, the high-ℓ wave packets maintain their coherence for periods ∼ 1 µs, i.e. for many hundreds of orbits. This coherence can be destroyed on sub-microsecond timescales by the application of even very small amounts of electrical noise at a rate that depends markedly on the spectral characteristics of the noise. In contrast, measurements over similar timescales with CO2 target gas densities of ∼ 1011 cm−3 provided no evidence of collisional dephasing. The mechanisms responsible for decoherence are discussed with the aid of classical and quantum simulations. The results of these simulations are in good accord with the experimental data.

Single-shot gas-phase thermometry using pure-rotational hybrid femtosecond/picosecond coherent anti-Stokes Raman scattering

High-repetition-rate, single-laser-shot measurements are important for the investigation of unsteady flows where temperature and species concentrations can vary significantly. Here, we demonstrate single-shot, pure-rotational, hybrid femtosecond/picosecond coherent anti-Stokes Raman scattering (fs/ps RCARS) thermometry based on a kHz-rate fs laser source. Interferences that can affect nanosecond (ns) and ps CARS, such as nonresonant background and collisional dephasing, are eliminated by selecting an appropriate time delay between the 100-fs pump/Stokes pulses and the pulse-shaped 8.4-ps probe. A time- and frequency-domain theoretical model is introduced to account for rotational-level dependent collisional dephasing and indicates that the optimal probe-pulse time delay is 13.5 ps to 30 ps. This time delay allows for uncorrected best-fit N2-RCARS temperature measurements with ~1% accuracy. Hence, the hybrid fs/ps RCARS approach can be performed with kHz-rate laser sources while avoiding corrections that can be difficult to predict in unsteady flows.

Optimal phase sensitivity of atomic Ramsey interferometers with coherent spin states

We present a detailed analysis of phase sensitivity for a nonlinear Ramsey interferometer, which utilize effective mean-field interaction of a two-component Bose-Einstein condensate in phase accumulation. For large enough particle number N and small phase shift ϕ, analytical results of the Ramsey signal and the phase sensitivity are derived for a product coherent state |θ, 0〉. When collisional dephasing is absent, we confirm that the optimal sensitivity scales as 2/N3/2 for polar angle of the initial state θ = π/4 or 3π/4. The best-sensitivity phase satisfies different transcendental equations, depending upon the initial state and the observable being measured after the phase accumulation. In the presence of the collisional dephasing, we show that the N−3/2-scaling rule of the sensitivity maintains with spin operators \(\hat J_x\) and \(\hat J_y\) measurements. A slightly better sensitivity is attainable for optimal coherent state with θ = π/6 or 5π/6.

Simultaneous electromagnetically induced transparency for two circularly polarized lasers coupled to the same linearly polarized laser in a four-level atomic system in the W scheme

Electromagnetic induced transparency (EIT) can be produced in a four-level atomic system in the W scheme using a linearly polarized optical field for simultaneously slowing down two $\ensuremath{\sigma}{}^{+}$ and $\ensuremath{\sigma}{}^{\ensuremath{-}}$ circularly polarized optical fields. This four-level atomic system can be set up with a $|{}^{1}{S}_{0}\ensuremath{\rangle}$ ground state and three Zeeman levels of the $|{}^{1}{P}_{1}\ensuremath{\rangle}$ excited state of any alkali-metal atom placed in a weak magnetic field. We apply our W scheme to ultracold magnesium atoms for neglecting the collisional dephasing. Atomic coherences are reported after solving a density matrix master equation including radiative relaxations from Zeeman states of the $|{}^{1}{P}_{1}\ensuremath{\rangle}$ multiplet to the $|{}^{1}{S}_{0}\ensuremath{\rangle}$ ground state. The EIT feature is analyzed using the transit time between the normal dispersive region and the EIT region. The evolution of the EIT feature with the variation of the coupling field is discussed using an intuitive dressed-state representation. We analyze the sensitivity of an EIT feature to pressure broadening of the excited Zeeman states.

Quantum-limited metrology in the presence of collisional dephasing

Including collisional decoherence explicitly, phase sensitivity for estimating effective scattering strength $\chi$ of a two-component Bose-Einstein condensate is derived analytically. With a measurement of spin operator $\hat{J}_{x}$, we find that the optimal sensitivity depends on initial coherent spin state. It degrades by a factor of $(2\gamma)^{1/3}$ below super-Heisenberg limit $\propto 1/N^{3/2}$ for particle number $N$ and the dephasing rate $1<\!<\gamma<N^{3/4}$. With a $\hat{J}_y$ measurement, our analytical results confirm that the phase $\phi=\chi t\sim 0$ can be detected at the limit even in the presence of the dephasing.

Electronic-resonance-enhanced coherent anti-Stokes Raman scattering of nitric oxide: Saturation and Stark effects

A theoretical analysis of electronic-resonance-enhanced (ERE) coherent anti-Stokes Raman scattering (CARS) of NO is described. The time-dependent density-matrix equations for the nonlinear ERE-CARS process are derived and manipulated into a form suitable for direct numerical integration. In the ERE-CARS configuration considered in this paper, the pump and Stokes beams are far from electronic-resonance. The visible 532 and 591 nm laser beams are used to excite Q-branch Raman resonances in the vibrational bands of the X (2)Pi electronic state of NO. An ultraviolet probe beam at 236 nm is used to excite P-, Q-, or R-branch transitions in the (v'=0, v"=1) band of the A (2)Sigma(+)-X (2)Pi electronic system of NO molecule. Experimental spectra are obtained either by scanning the ultraviolet probe beam while keeping the Stokes frequency fixed (probe scans) or by scanning the Stokes frequency while keeping the probe frequency fixed (Stokes scans). The calculated NO ERE-CARS spectra are compared with experimental spectra, and good agreement is observed between theory and experiment in terms of spectral peak locations and relative intensities. The effects of saturation of the two-photon Raman-resonant Q-branch transitions, the saturation of a one-photon electronic-resonant P-, Q-, or R-branch transitions in the A (2)Sigma(+)-X (2)Pi electronic system, and the coupling of these saturation processes are investigated. The coupling of the saturation processes for the probe and Raman transitions is complex and exhibits behavior similar to that observed in the electromagnetic induced transparency process. The probe scan spectra are significantly affected by Stark broadening due to the interaction of the pump and Stokes radiation with single-photon resonances between the upper vibration-rotation probe level in the A (2)Sigma(+) electronic levels and vibration-rotation levels in higher lying electronic levels. The ERE-CARS signal intensity is found to be much less sensitive to variations in the collisional dephasing rates under saturation conditions.

Picosecond time-resolved pure-rotational coherent anti-Stokes Raman spectroscopy for N_2 thermometry

Time-resolved pure-rotational coherent anti-Stokes Raman spectroscopy using picosecond-duration laser pulses is investigated for gas thermometry. The use of picosecond laser pulses significantly reduces background caused by scattering of the probe beam, and delayed probing of the Raman coherence enables elimination of interference from nonresonant four-wave mixing processes. Temperatures inferred from rotational spectra are sensitive to the probe delay because of the rotational-level dependence of collisional dephasing of Raman coherences. The sensitivity decreases, however, with increasing temperature, and accurate temperature measurements in a flame are demonstrated using a standard frequency-domain analysis of the spectra.

Electromagnetically induced transparency and slow light in three-level ladder systems: Effect of velocity-changing and dephasing collisions

We present a theory of electromagnetically induced transparency (EIT) and slow light in a Doppler broadened three-level ladder (cascade) system incorporating residual Doppler broadening of two-photon coherence and velocity-changing and dephasing collision effects of a buffer gas. Both regimes of wave-vector mismatch occurring when either the probe frequency is higher than that of the (strong) control field or vice versa are considered. It is found that the velocity-changing collisions in general cause narrowing of EIT resonance linewidths which, in a particular wave-vector mismatch regime, can lead to large transparency and slow light generation at relatively low control field intensities. Large collisional dephasing of two-photon coherence in a ladder system, however, tends to mask these effects. A reduction in group velocity by more than 3 orders of magnitude is predicted in the regime where the probe frequency is lesser than that of the control field and in the absence of collisions.