Monte Carlo Wave Function Research Articles

Quenching of the quantum p-strength in light exotic nuclei

One-nucleon spectroscopic overlaps, their strength or spectroscopic factors (SFs), and nucleon removal cross sections for light nuclei in the mass range A≤12 were evaluated using the fully correlated Quantum Monte Carlo (QMC) wave functions (WFs). Harder (AV18+UX) and softer (NV2+3) bare interactions were used providing consistent results. The SFs were also taken from simple Shell Model (SM) calculations. This structure information was incorporated in the standard three-body Faddeev/Alt-Grassberger-Sandhas reaction formalism to evaluate the (p,pN) cross sections. The results further our understanding of the quenching of the quantum p-shell strength obtained from structure and reactions. We have found the ratios of the total QMC sums of SFs to the SM ones to be uniform and ∼ 3/4. The corresponding ratios of the sums Below Particle Threshold (BPT) of SFs, as well as of total cross sections, deviate strikingly from the uniform trend in some special cases. We find these ratios to be close to unit for Li9→8Li+n and C9→8B+p. In contrast, they are strongly reduced for C11→10C+n and B11→10Be+p mirror transitions, resulting from the quenching of the strength for low-lying 2+ final state transitions. The QMC theoretical cross section BPT for C11(p,pn) is about two times smaller than the experimental data.

Transient responses of double core-holes generation in all-attosecond pump-probe spectroscopy

Double core-holes (DCHs) show remarkable and sensitive effects for understanding electron correlations and coherence. With advanced modulation of x-ray free-electron laser (XFEL) facility, we propose the forthcoming all-attosecond XFEL pump-probe spectroscopy can decipher the hidden photon-initiated dynamics of DCHs. The benchmark case of neon is investigated, and norm-nonconserving Monte-Carlo wavefunction method simulates non-Hermitian dynamics among vast states, which shows superiority in efficiency and reliability. In our scheme, population transfer to DCHs is sequentially irradiated by pump and probe laser. By varying time delay, Stark shifts and quantum path interference of resonant lines sensitively emerge at specific interval of two pulses. These ubiquitous multi-channel effects are also observed in phase-fluctuating pulses, derived from extra phases of impulsive Raman processes by pump laser. Non-perturbation absorption/emission verifies the uniquely interchangeable role of two pules in higher intensity. Our results reveal sensitive and robust responses on pulse parameters, which show potential capacity for XFEL attosecond pulse diagnosis and further attosecond-timescale chemical analysis.

Quantum Trajectories for Time-Local Non-Lindblad Master Equations.

For the efficient simulation of open quantum systems, we often use quantum jump trajectories given by pure states that evolve stochastically to unravel the dynamics of the underlying master equation. In the Markovian regime, when the dynamics is described by a Gorini-Kossakowski-Sudarshan-Lindblad (GKSL) master equation, this procedure is known as MonteCarlo wave function approach. However, beyond ultraweak system-bath coupling, the dynamics of the system is not described by an equation of GKSL type, but rather by the Redfield equation, which can be brought into pseudo-Lindblad form. Here, negative dissipation strengths prohibit the conventional approach. To overcome this problem, we propose a pseudo-Lindblad quantum trajectory (PLQT) unraveling. It does not require an effective extension of the state space, like other approaches, except for the addition of a single classical bit. We test the PLQT for the eternal non-Markovian master equation for a single qubit and an interacting Fermi-Hubbard chain coupled to a thermal bath and discuss its computational effort compared to solving the full master equation.

Facilitation of controllable excitation in Rydberg atomic ensembles

Strongly-interacting Rydberg atomic ensembles have shown intense collective excitation effects due to the inclusion of single Rydberg excitation shared by multiple atoms in the ensemble. In this paper we investigate a counter-intuitive Rydberg excitation facilitation with a strongly-interacting atomic ensemble in the strong probe-field regime, which is enabled by the role of a control atom nearby. Differing from the case of a single ensemble, we show that, the control atom's excitation adds to a second two-photon transition onto the doubly-excited Rydberg state, arising an excitation facilitation for the ensemble atoms. Our numerical studies depending on the method of quantum Monte Carlo wave function, exhibit the observation constraints of this excitation facilitation effect under practical experimental conditions. The results obtained can provide a flexible control for the excitation of Rydberg atomic ensembles and participate further uses in developing mesoscopic Rydberg gates for multiqubit quantum computation.

Phonon Blockade in Parametrically Pumped Acoustic Cavity at Finite Temperature

In this study, we investigated the phonon blockade effect in a parametrically driven and dissipative acoustic cavity at finite temperature. With the approximated analytical results based on the steady-state density-matrix master equation, we found that a quantum-interference-induced phonon blockade exists at finite temperature. We found a crossover between the quantum and thermal regimes on the curve of the second-order correlation function of the acoustic mode as the temperature increases. This phenomenon implies an asymmetry about the quantum and classic regimes. We also numerically simulated the single-phonon emission using the Monte Carlo wave function method. The results showed that a wide and deep dip around the zero time delay exists on the curve of the time-delayed second-order correlation function, which implies the possibility of observing a strong phonon blockade with pulse driving. Our study outlines a potential candidate for a efficient single-phonon source and applications in quantum information and phononic quantum networks.

Bottomonium observables in an open quantum system using the quantum trajectories method

We solve the Lindblad equation describing the Brownian motion of a Coulombic heavy quark-antiquark pair in a strongly coupled quark gluon plasma using the Monte Carlo wave function method. The Lindblad equation has been derived in the framework of pNRQCD and fully accounts for the quantum and non-Abelian nature of the system. The hydrodynamics of the plasma is realistically implemented through a 3+1D dissipative hydrodynamics code. We compute the bottomonium nuclear modification factor and elliptic flow and compare with the most recent LHC data. The computation does not rely on any free parameter, as it depends on two transport coefficients that have been evaluated independently in lattice QCD. Our final results, which include late-time feed down of excited states, agree well with the available data from LHC 5.02 TeV PbPb collisions.

Superradiance from nonideal initial states: A quantum trajectory approach

Collective emission behavior is usually described by the decay dynamics of the completely symmetric Dicke states. To study a more realistic scenario, we investigate alternative initial states inducing a more complex time evolution. Superposition states of the fully inverted Dicke state and the Dicke ground state with unequal mutual weights are studied as examples as well as superradiance stemming from atoms in clusters separated by more than one wavelength. The Monte Carlo wave function method serves as framework to study the dynamics of quantum states, which is determined by quantum jumps on the one hand and continuous evolution dynamics on the other hand. We compare this method with the classical picture of a system of rate equations written for the diagonal components of the density matrix.

Superradiantlike dynamics of nuclear spins by nonadiabatic electron shuttling

We investigate superradiantlike dynamics of a nuclear-spin bath in contact with an electron shuttle, modeled as a moving quantum dot trapping a single electron. The dot is shuttled between two external reservoirs, where electron-nuclear flip flops are associated with tunneling events. For an ideal model with uniform hyperfine interaction, realized through an isotopically enriched ``nuclear-spin island'', we discuss in detail the nuclear spin evolution and its relation to superradiance. We then show that the superradiantlike evolution is robust to various extensions of the initial setup, and derive the minimum shuttling time which allows to escape adiabatic spin evolution. We also discuss slow/fast shuttling under the inhomogeneous field of a nearby micromagnet and compare our scheme to a model with stationary quantum dot. Finally, we describe the electrical detection of nuclear entanglement in the framework of Monte Carlo wave-function simulations.

Steady states, squeezing, and entanglement in intracavity triplet down conversion

Triplet down conversion, the process of converting one high-energy photon into three low-energy photons, may soon be experimentally feasible in the optical regime, due to advances in optical resonator technology. We use quantum phase-space techniques to analyze the process of degenerate intracavity triplet down conversion by solving stochastic differential equations within the truncated positive-P representation. We simulate the time evolution of both intracavity fields, and examine the resulting steady-states as a function of the pump intensity. Quantum effects are most pronounced in the region immediately above the semi-classical pumping threshold, where our numerical results differ significantly from semi-classical predictions. We calculate steady-state fluctuation spectra and identify regimes of squeezing, bipartite entanglement, and non-Gaussianity measurable in the cavity output fields. We also validate the truncated positive-P description against Monte Carlo wave function simulations, finding good agreement for low mode populations.

Numerical evaluation of two-time correlation functions in open quantum systems with matrix product state methods: a comparison

We compare the efficiency of different matrix product state (MPS) based methods for the calculation of two-time correlation functions in open quantum systems. The methods are the purification approach[1] and two approaches[2,3] based on the Monte-Carlo wave function (MCWF) sampling of stochastic quantum trajectories using MPS techniques. We consider a XXZ spin chain either exposed to dephasing noise or to a dissipative local spin flip. We find that the preference for one of the approaches in terms of numerical efficiency depends strongly on the specific form of dissipation.

Monte-Carlo wavefunction approach for the spin dynamics of recombining radicals

We adapt the Monte-Carlo wavefunction (MCWF) approach to treat the open-system spin dynamics of radical pairs subject to spin-selective recombination reactions. For these systems, non-Lindbladian master equations are widely employed, which account for recombination via the non trace-preserving Haberkorn superoperator in combination with reaction-dependent exchange and singlet–triplet dephasing terms. We show that this type of master equation can be accommodated in the MCWF approach, by introducing a second type of quantum jump that accounts for the reaction simply by suitably terminating the propagation. In this way, we are able to evaluate approximate solutions to the time-dependent radical pair survival probability for systems that have been considered untreatable with the master equation approach until now. We explicate the suggested approach with calculations for radical pair reactions that have been suggested to be relevant for the quantum compass of birds and related phenomena.

A light weight regularization for wave function parameter gradients in quantum Monte Carlo

The parameter derivative of the expectation value of the energy, ∂E/∂p, is a key ingredient in variational Monte Carlo (VMC) wave function optimization methods. In some cases, a naïve estimate of this derivative suffers from an infinite variance, which inhibits the efficiency of optimization methods that rely on a stable estimate of the derivative. In this work, we derive a simple regularization of the naïve estimator, which is trivial to implement in existing VMC codes, has finite variance, and a negligible bias, which can be extrapolated to zero bias with no extra cost. We use this estimator to construct an unbiased, finite variance estimation of ∂E/∂p for a multi-Slater–Jastrow trial wave function on the LiH molecule and in the optimization of a multi-Slater–Jastrow trial wave function on the CuO molecule. This regularized estimator is a simple and efficient estimator of ∂E/∂p for VMC optimization techniques.

Many-body effects in (p,pN) reactions within a unified approach

We study knockout reactions with proton probes within a theoretical framework where ab initio Quantum Monte Carlo (QMC) wave functions are combined with the Faddeev/Alt-Grassberger-Sandhas few-body reaction formalism. QMC wave functions are used to describe 12C, yielding, for the first time, results consistent with the experimental root mean square (rms) point proton radii, (p,2p) total cross section data, as well as momentum distributions compatible with electron scattering data analysis. In our results for A≤12 and (N−Z)≤3 nuclei the ratios between the (i) theoretical cross sections evaluated using QMC and simple Shell Model structure inputs, and (ii) the corresponding ratios between the spectroscopic factors, summed over states below particle emission, are smaller than unity, pointing to the shortcomings of the simple Shell Model. This quenching is more significant for the knockout of the more correlated nucleon of the deficient species. These ratios can be represented reasonably well by a linear combination of the separation energy and the difference between the removed nucleon rms radius in the parent and residual nuclei, showing a mild dependence on these physical quantities.

Quantum Neimark-Sacker bifurcation

Recently, it has been demonstrated that asymptotic states of open quantum system can undergo qualitative changes resembling pitchfork, saddle-node, and period doubling classical bifurcations. Here, making use of the periodically modulated open quantum dimer model, we report and investigate a quantum Neimark-Sacker bifurcation. Its classical counterpart is the birth of a torus (an invariant curve in the Poincaré section) due to instability of a limit cycle (fixed point of the Poincaré map). The quantum system exhibits a transition from unimodal to bagel shaped stroboscopic distributions, as for Husimi representation, as for observables. The spectral properties of Floquet map experience changes reminiscent of the classical case, a pair of complex conjugated eigenvalues approaching a unit circle. Quantum Monte-Carlo wave function unraveling of the Lindblad master equation yields dynamics of single trajectories on “quantumtorus” and allows for quantifying it by rotation number. The bifurcation is sensitive to the number of quantum particles that can also be regarded as a control parameter.

Rydberg electromagnetically induced transparency in a large Hilbert space

We study Rydberg electromagnetically induced transparency (EIT) of cesium atoms in a magnetic field. The ladder level scheme consists of ground ($6{S}_{1/2}$), excited ($6{P}_{3/2}$), and Rydberg ($48{D}_{5/2}$) levels. The relevant 96 relevant magnetic sublevels are coupled to each other via coherent coupling and decay. A quantum Monte Carlo wave-function (QMCWF) approach is employed to solve the quantum master equation. The simulated EIT probe-absorption spectra and their magnetic-field dependence are compared with results of a cold-atom experiment, in which we perform an in situ, atom-based measurement of a rapidly decaying eddy-current magnetic field. The EIT spectrum in the magnetic field has two dominant lines with a Zeeman splitting of 5.6 MHz per gauss, which are employed to measure the magnetic field. The QMCWF results show good agreement with the experiment, exhibit additional spectroscopic features, and provide insights into the optical-pumping dynamics, radiation-pressure effects, and the relation of these phenomena with the EIT behavior.

Light-force-induced shift in laser spectroscopy of atomic helium

A laser-power-dependent shift has been observed in various atomic beam spectroscopy measurements, which was often treated by extrapolating the results to the zero-field limit. Here we present an experimental and theoretical study of this effect in the measurements of the $2{\phantom{\rule{0.16em}{0ex}}}^{3}S\ensuremath{-}2{\phantom{\rule{0.16em}{0ex}}}^{3}P$ transition frequency of $^{4}\mathrm{He}$. The light-force-induced shift was attributed as a result of modulated atomic trajectories induced by the standing-wave laser field and consequent distortions in the lineshape. Modulation of the beam spatial distributions was detected by imaging atoms at high laser power and was also simulated by the Monte Carlo wave-function approach. The nonlinear behavior of the light-force-shift was observed experimentally and reproduced by the simulations. The systematic shift in the extrapolated result at the zero-field limit was analyzed. As a consequence of this effect, a correction of +0.50(80) kHz was added to our previous result on the $2{\phantom{\rule{0.16em}{0ex}}}^{3}{S}_{1}\ensuremath{-}2{\phantom{\rule{0.16em}{0ex}}}^{3}{P}_{1}$ transition frequency [Phys. Rev. Lett. 119, 263002 (2017)], and the reevaluated value is 276 734 477 704.3(1.6) kHz.

Monte Carlo Wavefunction Approach to Singlet Fission Dynamics of Molecular Aggregates.

We have developed a Monte Carlo wavefunction (MCWF) approach to the singlet fission (SF) dynamics of linear aggregate models composed of monomers with weak diradical character. As an example, the SF dynamics for a pentacene dimer model is investigated by considering the intermolecular electronic coupling and the vibronic coupling. By comparing with the results by the quantum master equation (QME) approach, we clarify the dependences of the MCWF results on the time step (Δt) and the number of MC trajectories (MC). The SF dynamics by the MCWF approach is found to quantitatively (within an error of 0.02% for SF rate and of 0.005% for double-triplet (TT) yield) reproduce that by the QME approach when using a sufficiently small Δt (~0.03 fs) and a sufficiently large MC (~105). The computational time (treq) in the MCWF approach also exhibits dramatic reduction with increasing the size of aggregates (N-mers) as compared to that in the QME approach, e.g., ~34 times faster at the 20-mer, and the size-dependence of treq shows significant reduction from N5.15 (QME) to N3.09 (MCWF). These results demonstrate the promising high performance of the MCWF approach to the SF dynamics in extended multiradical molecular aggregates including a large number of quantum dissipation, e.g., vibronic coupling, modes.

The Monte Carlo wave-function method: A robust adaptive algorithm and a study in convergence

We present a stepwise adaptive-timestep version of the Quantum Jump (Monte Carlo wave-function) algorithm. Our method has proved to remain robust even for problems where the integrating implementation of the Quantum Jump method is numerically problematic. The only specific parameter of our algorithm is the single a priory parameter of the Quantum Jump method, the maximal allowed total jump probability per timestep. We study the convergence of ensembles of trajectories to the solution of the full master equation as a function of this parameter. This study is expected to pertain to any possible implementation of the Quantum Jump method.

Monte-Carlo simulations of superradiant lasing

We simulate the superradiant dynamics of ensembles of atoms in the presence of collective and individual atomic decay processes. We apply the Monte-Carlo wave-function method and identify quantum jumps in a reduced Dicke state basis, which reflects the permutation symmetry of the system. While the number of density matrix elements in the Dicke representation increases polynomially with atom number, the quantum jump dynamics populates only a single Dicke state at the time and thus efficient simulations can be carried out for tens of thousands of atoms. The superradiant pulses from initially excited atoms agree quantitatively with recent experimental results of strontium atoms but rapid atom loss in these experiments does not permit steady-state superradiance. By introducing an incident flux of new atoms to maintain a large average atom number, our theoretical calculations predict lasing with a millihertz linewidth despite rapid atom number fluctuations.

Interplay between optical pumping and Rydberg EIT in magnetic fields.

We perform Zeeman spectroscopy on a Rydberg electromagnetically induced transparency (EIT) system in a room-temperature Cs vapor cell, in magnetic fields up to 50 Gauss. The magnetic interactions of the |6S1/2 Fg = 4> ground, |6P3/2 Fe = 5> intermediate, and |33S1/2> Rydberg states that form the ladder-type EIT system are in the linear Zeeman, quadratic Zeeman, and the Paschen-Back regimes, respectively. We explain the dependence of Rydberg EIT spectra on the magnetic field and polarization. The asymmetry of the EIT spectra, which is caused by the quadratic Zeeman effect of the intermediate state, becomes paramount in magnetic fields ≥40 Gauss. We investigate the interplay between Rydberg EIT, which reduces photon scattering, and optical pumping, which relies on photon scattering. We employ a quantum Monte Carlo wave-function approach to quantitatively model the spectra and their asymmetry behavior. Simulated spectra are in good agreement with the experimental data.