Adiabatic Limit Research Articles

E to Z Photoisomerization of Phytochrome Cph1Δ Exceeds the Born-Oppenheimer Adiabatic Limit.

The Born-Oppenheimer adiabatic limit applies broadly in chemistry because most reactions occur on the ground electronic state. Photochemical reactions involve two or more electronic states and need not be subject to this adiabatic limit. The spectroscopic signatures of nonadiabatic processes are subtle, and therefore, experimental investigations have been limited to the few systems dominated by single photochemical outcomes. Systems with branched excited-state pathways have been neglected, despite their potential to reveal insights into photochemical reactivity. Here we present experimental evidence from coherent three-dimensional electronic spectroscopy that the E to Z photoisomerization of phytochrome Cph1 is strongly nonadiabatic, and the simulations reproduce the measured features only when the photoisomerization proceeds nonadiabatically near, but not through, a conical intersection. The results broaden the general understanding of photoisomerization mechanisms and motivate future studies of nonadiabatic processes with multiple outcomes arising from branching on excited-state potential energy surfaces.

Asymptotics of quantum channels: conserved quantities, an adiabatic limit, and matrix product states

This work derives an analytical formula for the asymptotic state---the quantum state resulting from an infinite number of applications of a general quantum channel on some initial state. For channels admitting multiple fixed or rotating points, conserved quantities---the left fixed/rotating points of the channel---determine the dependence of the asymptotic state on the initial state. The formula stems from a Noether-like theorem stating that, for any channel admitting a full-rank fixed point, conserved quantities commute with that channel’s Kraus operators up to a phase. The formula is applied to adiabatic transport of the fixed-point space of channels, revealing cases where the dissipative/spectral gap can close during any segment of the adiabatic path. The formula is also applied to calculate expectation values of noninjective matrix product states (MPS) in the thermodynamic limit, revealing that those expectation values can also be calculated using an MPS with reduced bond dimension and a modified boundary.

Breaking the quantum adiabatic speed limit by jumping along geodesics.

Quantum adiabatic evolutions find a broad range of applications in quantum physics and quantum technologies. The traditional form of the quantum adiabatic theorem limits the speed of adiabatic evolution by the minimum energy gaps of the system Hamiltonian. Here, we experimentally show using a nitrogen-vacancy center in diamond that, even in the presence of vanishing energy gaps, quantum adiabatic evolution is possible. This verifies a recently derived necessary and sufficient quantum adiabatic theorem and offers paths to overcome the conventionally assumed constraints on adiabatic methods. By fast modulation of dynamic phases, we demonstrate near-unit-fidelity quantum adiabatic processes in finite times. These results challenge traditional views and provide deeper understanding on quantum adiabatic processes, as well as promising strategies for the control of quantum systems.

A double-slit proposal for quantum annealing

We formulate and analyze a double-slit proposal for quantum annealing, which involves observing the probability of finding a two-level system (TLS) undergoing evolution from a transverse to a longitudinal field in the ground state at the final time tf. We demonstrate that for annealing schedules involving two consecutive diabatic transitions, an interference effect is generated akin to a double-slit experiment. The observation of oscillations in the ground state probability as a function of tf (before the adiabatic limit sets in) then constitutes a sensitive test of coherence between energy eigenstates. This is further illustrated by analyzing the effect of coupling the TLS to a thermal bath: increasing either the bath temperature or the coupling strength results in a damping of these oscillations. The theoretical tools we introduce significantly simplify the analysis of the generalized Landau-Zener problem. Furthermore, our analysis connects quantum annealing algorithms exhibiting speedups via the mechanism of coherent diabatic transitions to near-term experiments with quantum annealing hardware.

Analytic description of high-order harmonic generation in the adiabatic limit with application to an initial s state in an intense bicircular laser pulse

An analytic description of high-order harmonic generation (HHG) is proposed in the adiabatic (low-frequency) limit for an initial $s$ state and a laser field having an arbitrary wave form. The approach is based on the two-state time-dependent effective range theory and is extended to the case of neutral atoms and positively charged ions by introducing ad hoc the Coulomb corrections for HHG. The resulting closed analytical form for the HHG amplitude is discussed in terms of real classical trajectories. The accuracy of the results of our analytic model is demonstrated by comparison with numerical solutions of the time-dependent Schr\odinger equation for a strong bicircular field composed of two equally intense components with carrier frequencies $\ensuremath{\omega}$ and $2\ensuremath{\omega}$ and opposite helicities. In particular, we demonstrate the effect of ionization gating on HHG in a bicircular field, both for the case that the two field components are quasimonochromatic and for the case that the field components are time-delayed short pulses. We show how ionization in a strong laser field not only smooths the usual peak structures in HHG spectra but also changes the positions and polarization properties of the generated harmonics, seemingly violating the standard dipole selection rules. These effects appear for both short and long incident laser pulses. In the case of time-delayed short laser pulses, ionization gating provides an effective tool for control of both the HHG yield and the harmonic polarizations [Frolov et al., Phys. Rev. Lett. 120, 263203 (2018)]. For the case of short laser pulses, we introduce a simple two-dipole model that captures the physics underlying the harmonic emission process, describing both the oscillation patterns in HHG spectra and also the dependence of the harmonic polarizations on the harmonic energy.

Electric Current Fluctuations Induced by Molecular Vibrations in the Adiabatic Limit: Molecular Dynamics-Driven Liouville von Neumann Approach

We investigate time-dependent electron transport through a molecular junction in the adiabatic limit at the density-functional tight-binding level using the molecular dynamics-driven Liouville von ...

Influence of hydrogen addition to pipeline natural gas on the combustion performance of a cooktop burner

Displacing pipeline natural gas with renewable hydrogen is a promising way to reduce the emission of carbon dioxide, which is a major greenhouse gas. However, due to significantly differing characteristics of hydrogen and natural gas, such as flame speed, adiabatic flame temperature and stability limits, the combustion performance of hydrogen/natural gas mixture differs from pure natural gas. From the perspective of residential end users, a key question is: how much hydrogen can be injected into the pipeline natural gas without influencing the performance of the residential burners? A representative cooktop burner is selected to study the influence of hydrogen addition on the combustion and cooking performance. Flashback limits, ignition time, flame characteristics, cooking performance, combustion noise, burner temperature, and various emissions (NO, NO2, N2O, CO, unburned hydrocarbon (UHC), NH3) are evaluated for different levels of hydrogen addition. According to the experimental results, the combustion performance of the cooktop burner is not significantly affected with up to about 15% hydrogen addition by volume, which shows the feasibility of utilizing hydrogen on existing cooking appliances without any modification. The experiment methodologies and results in this study will serve as a reference for future test and emission regulation standards on domestic burners.

Geometric Phase of Linear Cosmological Perturbations in Two-Field Inflation

As a footprint of primordial perturbations in cosmological observations, the Berry phase of cosmological perturbations can serve to probe the cosmological inflation. Considering linear perturbations in two-field slow-roll inflation, we derive the Hamiltonians of the scalar and tensor Fourier modes in the form of time-dependent harmonic oscillator Hamiltonians. We find the invariant operators of the resulting Hamiltonians and use these invariants to calculate the Berry phase for sub-horizon scalar and tensor modes in the adiabatic limit.

An extension of the fewest switches surface hopping algorithm to complex Hamiltonians and photophysics in magnetic fields: Berry curvature and "magnetic" forces.

We present a preliminary extension of the fewest switches surface hopping (FSSH) algorithm to the case of complex Hamiltonians as appropriate for modeling the dynamics of photoexcited molecules in magnetic fields. We make ansätze for the direction of momentum rescaling, and we account for Berry's phase effects through "magnetic" forces as applicable in the adiabatic limit. Because Berry's phase is a nonlocal, topological characteristic of a set of entangled potential energy surfaces, we find that Tully's local FSSH algorithm can only partially capture the correct physics.

Classical stochastic systems with fast-switching environments: Reduced master equations, their interpretation, and limits of validity.

We study classical Markovian stochastic systems with discrete states, coupled to randomly switching external environments. For fast environmental processes we derive reduced dynamics for the system itself, focusing on corrections to the adiabatic limit of infinite timescale separation. We show that this can lead to master equations with bursting events. Negative transition rates can result in the reduced master equation, leading to unphysical short-time behavior. However, the reduced master equation can describe stationary states better than a leading-order adiabatic calculation, similar to what is known for Kramers-Moyal expansions in the context of the Pawula theorem [R. F. Pawula, Phys. Rev. 162, 186 (1967)PHRVAO0031-899X10.1103/PhysRev.162.186; H. Risken and H. Vollmer, Z. Phys. B 35, 313 (1979)ZPBBDJ0340-224X10.1007/BF01319854]. We provide an interpretation of the reduced dynamics in discrete time and a criterion for the occurrence of negative rates for systems with two environmental states.

Model reduction methods for population dynamics with fast-switching environments: Reduced master equations, stochastic differential equations, and applications.

We study stochastic population dynamics coupled to fast external environments and combine expansions in the inverse switching rate of the environment and a Kramers-Moyal expansion in the inverse size of the population. This leads to a series of approximation schemes, capturing both intrinsic and environmental noise. These methods provide a means of efficient simulation and we show how they can be used to obtain analytical results for the fluctuations of population dynamics in switching environments. We place the approximations in relation to existing work on piecewise-deterministic and piecewise-diffusive Markov processes. Finally, we demonstrate the accuracy and efficiency of these model-reduction methods in different research fields, including systems in biology and a model of crack propagation.

Nonadiabatic dynamics and geometric phase of an ultrafast rotating electron spin

The spin in a rotating frame has attracted a lot of attentions recently, as it deeply relates to both fundamental physics such as pseudo-magnetic field and geometric phase, and applications such as gyroscopic sensors. However, previous studies only focused on adiabatic limit, where the rotating frequency is much smaller than the spin frequency. Here we propose to use a levitated nano-diamond with a built-in nitrogen-vacancy (NV) center to study the dynamics and the geometric phase of a rotating electron spin without adiabatic approximation. We find that the transition between the spin levels appears when the rotating frequency is comparable to the spin frequency at zero magnetic field. Then we use Floquet theory to numerically solve the spin energy spectrum, study the spin dynamics and calculate the geometric phase under a finite magnetic field, where the rotating frequency to induce resonant transition could be greatly reduced.

Experimental Realization of Nonadiabatic Shortcut to Non-Abelian Geometric Gates

When a quantum system is driven slowly through a parametric cycle in a degenerate Hilbert space, the state would acquire a non-Abelian geometric phase, which is stable and forms the foundation for holonomic quantum computation (HQC). However, in the adiabatic limit, the environmental decoherence becomes a significant source of errors. Recently, various nonadiabatic holonomic quantum computation (NHQC) schemes have been proposed, but all at the price of increased sensitivity to control errors. Alternatively, there exist theoretical proposals for speeding up HQC by the technique of "shortcut to adiabaticity" (STA), but no experimental demonstration has been reported so far, as these proposals involve a complicated control of four energy levels simultaneously. Here, we propose and experimentally demonstrate that HQC via shortcut to adiabaticity can be constructed with only three energy levels, using a superconducting qubit in a scalable architecture. With this scheme, all holonomic single-qubit operations can be realized nonadiabatically through a single cycle of state evolution. As a result, we are able to experimentally benchmark the stability of STA+HQC against NHQC in the same platform. The flexibility and simplicity of our scheme makes it also implementable on other systems, such as nitrogen-vacancy center, quantum dots, and nuclear magnetic resonance. Finally, our scheme can be extended to construct two-qubit holonomic entangling gates, leading to a universal set of STAHQC gates.

Quantum particle in a split box: Excitations to the ground state

We discuss two different approaches for splitting the wavefunction of a single-particle-box (SPB) into two equal parts. Adiabatic insertion of a barrier in the center of a SPB in order to make two compartments which each have probability 1/2 to find the particle in it is one of the key steps for a Szilard engine. However, any asymmetry between the volume of the compartments due to an off-center insertion of the barrier results in a particle that is fully localized in the larger compartment, in the adiabatic limit. We show that rather than exactly splitting the eigenfunctions in half by a symmetric barrier, one can use a non-adiabatic insertion of an asymmetric barrier to induce excitations to the first excited state of the full box. As the barrier height goes to infinity the excited state of the full box becomes the ground state of one of the new boxes. Thus, we can achieve close to exact splitting of the probability between the two compartments using the more realistic non-adiabatic, not perfectly centered barrier, rather than the idealized adiabatic and central barrier normally assumed.

Nonequilibrium dynamics of superconductivity in the attractive Hubbard model

We present a framework of semiclassical superconductivity (SC) dynamics that properly includes effects of spatial fluctuations for the attractive Hubbard model. We consider both coherent and adiabatic limits. To model the coherent SC dynamics, we develop a real-space von~Neumann equation based on the time-dependent Hartree-Fock-Bogoliubov theory. Applying our method to interaction quenches in the negative-$U$ Hubbard model, we show that the relaxation of SC order at weak coupling is dominated by Landau-damping. At strong coupling, we find a two-stage relaxation of the pairing field: a collapse of the synchronized oscillation of Cooper pairs due to spatial inhomogeneity, followed by a slow relaxation to a quasi-stationary state. SC dynamics in adiabatic limit is described by a quantum Landau-Lifshitz equation with Ginzburg-Landau relaxation. Numerical simulations of the pump-probe process show that long time recovery of the pairing field is dominated by defects dynamics. Our results demonstrate the important role of spatial fluctuations in both limits.

A new complete Calabi\u2013Yau metric on {mathbb {C}}^3

Motivated by the study of collapsing Calabi–Yau 3-folds with a Lefschetz K3 fibration, we construct a complete Calabi–Yau metric on {mathbb {C}}^3 with maximal volume growth, which in the appropriate scale is expected to model the collapsing metric near the nodal point. This new Calabi–Yau metric has singular tangent cone at infinity {mathbb {C}}^2/{mathbb {Z}}_2 times {mathbb {C}}, and its Riemannian geometry has certain non-standard features near the singularity of the tangent cone, which are more typical of adiabatic limit problems. The proof uses an existence result in H-J. Hein’s Ph.D. thesis to perturb an asymptotic approximate solution into an actual solution, and the main difficulty lies in correcting the slowly decaying error terms.

Noise-induced rectification in out-of-equilibrium structures.

We consider the motion of overdamped particles over random potentials subjected to a Gaussian white noise and a time-dependent periodic external forcing. The random potential is modeled as the potential resulting from the interaction of a point particle with a random polymer. The random polymer is made up, by means of some stochastic process, from a finite set of possible monomer types. The process is assumed to reach a nonequilibrium stationary state, which means that every realization of a random polymer can be considered as an out-of-equilibrium structure. We show that the net flux of particles over this random medium is nonvanishing when the potential profile on every monomer is symmetric. We prove that this ratchetlike phenomenon is a consequence of the irreversibility of the stochastic process generating the polymer. On the contrary, when the process generating the polymer is at equilibrium (thus fulfilling the detailed balance condition) the system is unable to rectify the motion. We calculate the net flux of the particles in the adiabatic limit for a simple model and we test our theoretical predictions by means of Langevin dynamics simulations. We also show that, out of the adiabatic limit, the system also exhibits current reversals as well as nonmonotonic dependence of the diffusion coefficient as a function of forcing amplitude.

Strong electron-phonon coupling, electron-hole asymmetry, and nonadiabaticity in magic-angle twisted bilayer graphene

We report strong electron-phonon coupling in magic-angle twisted bilayer graphene (MA-TBG) obtained from atomistic description of the system including more than 10000 atoms in the moire supercell. Electronic structure, phonon spectrum, and electron-phonon coupling strength lambda are obtained before and after atomic-position relaxation both in and out of plane. Obtained lambda is very large for MA-TBG, with lambda > 1 near the half-filling energies of the flat bands, while it is small (lambda ~ 0.1) for monolayer and unrotated bilayer graphene. Significant electron-hole asymmetry occurs in the electronic structure after atomic-structure relaxation, so lambda is much stronger with hole doping than electron doping. Obtained electron-phonon coupling is nearly isotropic and depends very weakly on electronic band and momentum, indicating that electron-phonon coupling prefers single-gap s-wave superconductivity. Relevant phonon energies are much larger than electron energy scale, going far beyond adiabatic limit. Our results provide a fundamental understanding of the electron-phonon interaction in MA-TBG, highlighting that it can contribute to rich physics of the system.

Photoelectrons Are Not Always Quite Free.

The photoelectron spectra of Sm2O- obtained over a range of photon energies exhibit anomalous changes in relative excited-state band intensities. Specifically, the excited-state transition intensities increase relative to the transition to the neutral ground state with decreasing photon energy, the opposite of what is expected from threshold effects. This phenomenon was previously observed in studies on several Sm-rich homo- and heterolanthanide oxides collected with two different harmonic outputs of a Nd:YAG (2.330 and 3.495 eV) [ J. Chem. Phys. 2017, 146, 194310]. We relate these anomalous intensities to populations of ground and excited anionic and neutrals states through the inspection of time-dependent perturbation theory within the adiabatic and sudden limits and for the first time show that transition intensities in photoelectron spectroscopy have a deep significance in gauging participation from excited states. We believe our results will have significance in the study of other electron-rich systems that have especially high density of accessible spin states.

Torsionally induced exciton localization and decoherence in π-conjugated polymers.

We develop a model of excitons coupled to the rotational motion of monomers to study the torsionally induced relaxation and decoherence of excitons in π-conjugated polymers. The model assumes that the monomer units are described by elastically uncoupled harmonic oscillators and that there is a linear exciton-roton coupling. Although the rotational degrees of freedom are much slower than the exciton, so that the adiabatic approximation is generally expected to be valid, we also investigate possible quantized roton corrections via coupled time evolving block decimation-Ehrenfest equations of motion. For the relaxation of the lowest-excited exciton, we find that (1) for a polymer chain with a ground state spiral torsional conformation, the equilibrium angular displacement of each monomer is proportional to the difference of the exciton bond-orders on the neighboring bridging bonds. Consequently, this displacement vanishes in the long chain limit and a classical (Landau) exciton-polaron is not formed. (2) For a polymer chain with a ground state staggered torsional conformation, the equilibrium angular displacement of each monomer is proportional to the sum of the exciton bond-orders on the neighboring bridging bonds. Consequently, there is significant angular displacement and local planarization causing exciton density localization. A classical (Landau) exciton-polaron is formed where the staggered angular displacement is proportional to the exciton density. (3) Generally, in the adiabatic limit, the decay of off-diagonal long-range order (i.e., exciton decoherence) mirrors the localization of the exciton density. However, quantum corrections to the rotational motion alter this adiabatic prediction because of correlated exciton-roton dynamics within the first rotational half-period. In particular, exciton-polaron quasiparticle formation causes more rapid and oscillatory exciton decoherence and slower exciton density localization.