Generalized pi pulses

Computing Quantum Mean Values in the Deep Chaotic Regime

We study the time evolution of mean values of quantum operators in a regime plagued by two difficulties: the smallness of ℏ and the presence of strong and ubiquitous classical chaos. While numerics become too computationally expensive for purely quantum calculations as ℏ→0, methods that take advantage of the smallness of ℏ-that is, semiclassical methods-suffer from both conceptual and practical difficulties in the deep chaotic regime. We implement an approach which addresses these conceptual problems, leading to a deeper understanding of the origin of the interference contributions to the operator's mean value. We show that in the deep chaotic regime our approach is capable of unprecedented accuracy, while a standard semiclassical method (the Herman-Kluk propagator) produces only numerical noise. Our work paves the way to the development and employment of more efficient and accurate methods for quantum simulations of systems with strongly chaotic classical limits.

Funneling dynamics in a phenylacetylene trimer: Coherent excitation of donor excitonic states and their superposition

Funneling dynamics in conjugated dendrimers has raised great interest in the context of artificial light-harvesting processes. Photoinduced relaxation has been explored by time-resolved spectroscopy and simulations, mainly by semiclassical approaches or referring to open quantum systems methods, within the Redfield approximation. Here, we take the benefit of an ab initio investigation of a phenylacetylene trimer, and in the spirit of a divide-and-conquer approach, we focus on the early dynamics of the hierarchy of interactions. We build a simplified but realistic model by retaining only bright electronic states and selecting the vibrational domain expected to play the dominant role for timescales shorter than 500 fs. We specifically analyze the role of the in-plane high-frequency skeletal vibrational modes involving the triple bonds. Open quantum system non-adiabatic dynamics involving conical intersections is conducted by separating the electronic subsystem from the high-frequency tuning and coupling vibrational baths. This partition is implemented within a robust non-perturbative and non-Markovian method, here the hierarchical equations of motion. We will more precisely analyze the coherent preparation of donor states or of their superposition by short laser pulses with different polarizations. In particular, we extend the π-pulse strategy for the creation of a superposition to a V-type system. We study the relaxation induced by the high-frequency vibrational collective modes and the transitory dissymmetry, which results from the creation of a superposition of electronic donor states.

Work statistics in the periodically driven quartic oscillator: Classical versus quantum dynamics

In the thermodynamics of nanoscopic systems, the relation between classical and quantum mechanical description is of particular importance. To scrutinize this correspondence we study an anharmonic oscillator driven by a periodic external force with slowly varying amplitude both classically and within the framework of quantum mechanics. The energy change of the oscillator induced by the driving is closely related to the probability distribution of work for the system. With the amplitude λ(t) of the drive increasing from zero to a maximum λ_{max} and then going back to zero again, the initial and final Hamiltonian coincide. The main quantity of interest is then the probability density P(E_{f}|E_{i}) for transitions from initial energy E_{i} to final energy E_{f}. In the classical case nondiagonal transitions with E_{f}≠E_{i} mainly arise due to the mechanism of separatrix crossing. We show that approximate analytical results within the pendulum approximation are in accordance with numerical simulations. In the quantum case numerically exact results are complemented with analytical arguments employing Floquet theory. For both the classical and quantum case we provide an intuitive explanation for the periodic variation of P(E_{f}|E_{i}) with the maximal amplitude λ_{max} of the driving.

Periodic thermodynamics of the Rabi model with circular polarization for arbitrary spin quantum numbers

We consider a spin s subjected to both a static and an orthogonally applied oscillating, circularly polarized magnetic field while being coupled to a heat bath and analytically determine the quasistationary distribution of its Floquet-state occupation probabilities for arbitrarily strong driving. This distribution is shown to be Boltzmannian with a quasitemperature which is different from the temperature of the bath and independent of the spin quantum number. We discover a remarkable formal analogy between the quasithermal magnetism of the nonequilibrium steady state of a driven ideal paramagnetic material and the usual thermal paramagnetism. Nonetheless, the response of such a material to the combined fields is predicted to show several unexpected features, even allowing one to turn a paramagnet into a diamagnet under strong driving. Thus, we argue that experimental measurements of this response may provide key paradigms for the emerging field of periodic thermodynamics.

Anomalous Rabi Oscillations in Multilevel Quantum Systems

We show that the excitation probability of a state within a manifold of levels undergoes Rabi oscillations with the frequency determined by the energy difference between the states and not by the pulse area, for sufficiently strong pulses. The population and coherence remains in the two-level subsystem formed by the initial and target state even at Rabi frequencies exceeding the energy difference. The observed dynamics can be useful in nonlinear spectroscopy and quantum state preparation.

Energy flow in periodic thermodynamics

A key quantity characterizing a time-periodically forced quantum system coupled to a heat bath is the energy flowing in the steady state through the system into the bath, where it is dissipated. We derive a general expression which allows one to compute this energy dissipation rate for a heat bath consisting of a large number of harmonic oscillators and work out two analytically solvable model examples. In particular, we distinguish between genuine transitions effectuating a change of the systems's Floquet state and pseudotransitions preserving that state; the latter are shown to yield an important contribution to the total dissipation rate. Our results suggest possible driving-mediated heating and cooling schemes on the quantum level. They also indicate that a driven system does not necessarily occupy only a single Floquet state when in contact with a zero-temperature bath.

Effect of laser pulse shaping parameters on the fidelity of quantum logic gates

The effect of varying parameters specific to laser pulse shaping instruments on resulting fidelities for the ACNOT(1), NOT(2), and Hadamard(2) quantum logic gates are studied for the diatomic molecule (12)C(16)O. These parameters include varying the frequency resolution, adjusting the number of frequency components and also varying the amplitude and phase at each frequency component. A time domain analytic form of the original discretized frequency domain laser pulse function is derived, providing a useful means to infer the resulting pulse shape through variations to the aforementioned parameters. We show that amplitude variation at each frequency component is a crucial requirement for optimal laser pulse shaping, whereas phase variation provides minimal contribution. We also show that high fidelity laser pulses are dependent upon the frequency resolution and increasing the number of frequency components provides only a small incremental improvement to quantum gate fidelity. Analysis through use of the pulse area theorem confirms the resulting population dynamics for one or two frequency high fidelity laser pulses and implies similar dynamics for more complex laser pulse shapes. The ability to produce high fidelity laser pulses that provide both population control and global phase alignment is attributed greatly to the natural evolution phase alignment of the qubits involved within the quantum logic gate operation.

OPTIMALLY CONTROLLED VIBRATIONAL POPULATION TRANSFER IN A DIATOMIC QUANTUM SYSTEM

A time-dependent formulation of quantum control is employed to investigate optimally controlled vibrational population transfer in a diatomic quantum system. The problem of finding the optimal laser field needed to achieve a specific quantum transition from an initial state to the desired target goal is formulated using an iterative method and the conjugate gradient method (CGM). The time-dependent Schrödinger equation is solved with interaction of laser radiation with matter included within a dipole approximation in the Hamiltonian. Appropriate boundary conditions are chosen for the evolution problem. The control objective is chosen as the value of transition probability from an initial state to a target state. A comparison is made between the results obtained using the iterative method and the CGM for optimization. Finally, quantum bits are encoded using the vibrational states of the diatomic in the regime of low-vibrational excitation.

Pulse-train control of branching processes: elimination of background and intruder state population

The authors introduce and describe pulse train control (PTC) of population branching in strongly coupled processes as a novel control tool for the separation of competing multiphoton processes. Control strategies are presented based on the different responses of processes with different photonicities and/or different frequency detunings to the pulse-to-pulse time delay and the pulse-to-pulse phase shift in pulse trains. The control efficiency is further enhanced by the property of pulse trains that complete population transfer can be obtained over an extended frequency range that replaces the resonance frequency of simple pulses. The possibility to freely tune the frequency assists the separation of the competing processes and reduces the number of subpulses required for full control. As a sample application, PTC of leaking multiphoton resonances is demonstrated by numerical simulations. In model systems exhibiting sizable background (intruder) state population if excited with single pulses, PTC leading to complete accumulation of population in the target state and elimination of background population is readily achieved. The analysis of the results reveals different mechanisms of control and provides clues on the mechanisms of the leaking process itself. In an alternative setup, pulse trains can be used as a phase-sensitive tool for level switching. By changing only the pulse-to-pulse phase shift of a train with otherwise unchanged parameters, population can be transferred to any of two different target states in a near-quantitative manner.

Coherent control of molecular alignment of homonuclear diatomic molecules by analytically designed laser pulses

We present an analytic scheme for designing laser pulses to manipulate the field-free molecular alignment of a homonuclear diatomic molecule. The scheme is based on the use of a generalized pulse-area theorem and makes use of pulses constructed around two-photon resonant frequencies. In the proposed scheme, the populations and relative phases of the rovibrational states of the molecule are independently controlled utilizing changes in the laser intensity and in the carrier-envelope phase difference, respectively. This allows us to create the correct coherent superposition of rovibrational states needed to achieve optimal molecular alignment. The validity and efficiency of the scheme are demonstrated by explicit application to the H(2) molecule. The analytically designed laser pulses are tested by exact numerical solutions of the time-dependent Schrodinger equation including laser-molecule interactions to all orders of the field strength. The design of a sequence of pulses to further enhance molecular alignment is also discussed and tested. It is found that the rotating wave approximation used in the analytic design of the laser pulses leads to small errors in the prediction of the relative phase of the rotational states. It is further shown how these errors may be easily corrected.

Quantum computing based on vibrational eigenstates: pulse area theorem analysis

In a recent paper [D. Babikov, J. Chem. Phys. 121, 7577 (2004)], quantum optimal control theory was applied to analyze the accuracy of quantum gates in a quantum computer based on molecular vibrational eigenstates. The effects of the anharmonicity parameter of the molecule, the target time of the pulse, and the penalty function on the accuracy of the qubit transformations were investigated. We demonstrate that the effects of all the molecular and laser-pulse parameters can be explained utilizing the analytical pulse area theorem, which originates from the standard two-level model. Moreover, by analyzing the difference between the optimal control theory results and those obtained using the pulse area theorem, it is shown that extremely high quantum gate fidelity can be achieved for a qubit system based on vibrational eigenstates.

Counterdiabatic suppression of background state population in resonance leaking by controlling intermediate branching

The counterdiabatic principle [M. Demirplak and S. A. Rice, J. Phys. Chem. A 107, 9937 (2003)] is used in a pragmatic way to formulate a practical control strategy for perturbed population transfer. Interpreting the appearance of population in undesirable intruder or background states as phenomenological consequences of diabatic perturbations, such branching is suppressed as soon as it arises. By invoking a penalty term that is sensitive to any transitional population in undesirable levels, a correction field is created which effectively prevents diabatic behavior. This strategy is applied to the control of background state population in multiphoton excitations. For a model five-level system we show that leaking of a resonant three-photon transition to a background state can readily be suppressed by simple correction fields obtained from our intermediate-branching driven implementation of counterdiabatic control.

Pulse-pair control of resonance leaking in molecular multiphoton transitions

We use model five-level systems to study resonance leaking of pi-pulse-induced multiphoton (MP) transitions along a strongly coupled anharmonic ladder. We demonstrate that the presence of a weakly bound background state attached to the ladder either in linear or Lambda configuration can have very pronounced effects on resonant MP ladder transitions, including essentially complete quenching of the primary transition. We also develop control strategies for the elimination of background state population based on phase-adjusted Gaussian pulse pairs and discuss the underlying control mechanisms. Finally we show that these strategies are effective in realistic molecular many-level systems. In particular, we demonstrate efficient pulse-pair control of resonance leaking in a 165-level system modeling vibrational excitation in HCN.