Joint Center for Quantum Information and Computer Science, NIST/University of Maryland（量子信息与计算机联合中心，美国国家标准与技术研究院/马里兰大学）；Institute of Science and Technology Austria（奥地利科学技术研究所）；Department of Physics, University of Colorado, Boulder（科罗拉多大学博尔德分校物理系）；JILA, NIST/University of Colorado（JILA，美国国家标准与技术研究院/科罗拉多大学）
Victor V. Albert, Eric Kubischta, Mikhail Lemeshko, Lee R. Liu
We formulate a quantum phase space for rotational and nuclear-spin states of rigid molecules. For each nuclear spin isomer, we re-derive the isomer's admissible angular momentum states from molecular geometry and nuclear-spin data, introduce its angular position states using quantization theory, and develop a generalized Fourier transform converting between the two. We classify molecules into three types -- asymmetric, rotationally symmetric, and perrotationally symmetric -- with the last type having no macroscopic analogue due to nuclear-spin statistics constraints. We discuss two general features in perrotationally symmetric state spaces that are Hamiltonian-independent and induced solely by symmetry and spin statistics. First, we quantify when and how an isomer's state space is completely rotation-spin entangled, meaning that it does not admit any separable states. Second, we identify isomers whose position states house an internal pseudo-spin or "fiber" degree of freedom, and the fiber's Berry phase or matrix after adiabatic changes in position yields naturally robust operations, akin to braiding anyonic quasiparticles or realizing fault-tolerant quantum gates. We outline how the fiber can be used as a quantum error-correcting code and discuss scenarios where these features can be experimentally probed
Control of molecular rotations by laser fields is an active area of research focusing on the alignment/orientation of otherwise isotropic molecular samples. Oriented molecules are useful in many applications, such as molecular orbital tomography, femtosecond imaging of molecular structure, dynamics and chemical reaction control. In this work, we present a novel, previously unreported phenomenon appearing in thermal ensembles of non-linear polar molecules excited by a single THz pulse. We find that the induced orientation lasts long after the excitation pulse is over. In the case of symmetric-t…
We demonstrate strong laser-field-free orientation of absolute-ground-state carbonyl sulfide molecules. The molecules are oriented by the combination of a 485-ps-long non-resonant laser pulse and a weak static electric field. The edges of the laser pulse create a coherent superposition of two rotational states resulting in revivals of strong transient molecular orientation after the laser pulse. The experimentally attained degree of orientation of 0.6 corresponds to the theoretical maximum for mixing of the two states. Switching off the dc field would provide the same orientation completely fi…
Ultrashort laser pulses are widely used for transient field-free molecular orientation -- a phenomenon important in chemical reaction dynamics, ultrafast molecular imaging, high harmonics generation, and attosecond science. However, significant molecular orientation usually requires rotationally cold molecules, like in rarified molecular beams, because chaotic thermal motion is detrimental to the orientation process. Here we propose to use the mechanism of the echo phenomenon previously observed in hadron accelerators, free-electron lasers, and laser-excited molecules to overcome the destructi…
Significant molecular orientation can be achieved by time-symmetric single-cycle pulses of zero area, in the THz region. We show that in spite of the existence of a combined time-space symmetry operation, not only large peak instantaneous orientations but also nonzero time-average orientations over a rotational period can be obtained. We show that this unexpected phenomenon is due to interferences among eigenstates of the time-evolution operator, as was described previously for transport phenomena in quantum ratchets. This mechanism also works for sequences of identical pulses, spanning a rota…
We apply two recent generalizations of monotonically convergent optimization algorithms to the control of molecular orientation by laser fields. We show how to minimize the control duration by a step-wise optimization and maximize the field-free molecular orientation using state-dependent constraints. We discuss the physical relevance of the different results.
We study the control by electromagnetic fields of molecular alignment and orientation, in a linear, rigid rotor model. With the help of a monotonically convergent algorithm, we find that the optimal field is in the microwave part of the spectrum and acts by resonantly exciting the rotation of the molecule progressively from the ground state, i.e., by rotational ladder climbing. This mechanism is present not only when maximizing orientation or alignment, but also when using prescribed target states that simultaneously optimize the efficiency of orientation/alignment and its duration. The extens…
The constraint of time-integrated zero-area on the laser field is a fundamental, both theoretical and experimental requirement in the control of molecular dynamics. By using techniques of local and optimal control theory, we show how to enforce this constraint on two benchmark control problems, namely molecular orientation and photofragmentation. The origin and the physical implications on the dynamics of this zero-area control field are discussed.
We investigate to which extend a THz laser pulse can be used to produce field-free molecular orientation at high temperature. We consider laser pulses that can be implemented with the state of the art technology and we show that the efficiency of the control scheme crucially depends on the parameters of the molecule. We analyze the temperature effects on molecular dynamics and we demonstrate that, for some molecules, a noticeable orientation can be achieved at high temperature.
We demonstrate and explore an all-optical technique for direct monitoring the orientation dynamics of gas phase molecular ensembles. The technique termed 'MOISH' utilizes the transiently lifted inversion symmetry of polar gas media and provides a sensitive and spatially localized probing of second harmonic generation signal that is directly correlated with the orientation of the gas. Our experimental results reveal selective electronic and nuclear dynamical contributions to the overall nonlinear optical signal and decipher them apart using the "reporter gas" approach. 'MOISH' provides new, cru…
We apply a time-dependent perturbation theory based on unitary transformations combined with averaging techniques, on molecular orientation dynamics by ultrashort pulses. We test the validity and the accuracy of this approach on LiCl described within a rigid-rotor model and find that it is more accurate than other approximations. Furthermore, it is shown that a noticeable orientation can be achieved for experimentally standard short laser pulses of zero time average. In this case, we determine the dynamically relevant parameters by using the perturbative propagator, that is derived from this s…
The question of classicality is addressed in relation with the shape of the nuclear skeleton of molecular systems. As the most natural environment, the electrons of the molecule are considered as continuously monitoring agents for the nuclei. For this picture, an elementary formalism of decoherence theory is developed and numerical results are presented for few-particle systems. The numerical examples suggest that the electron-nucleus Coulomb interaction is sufficient for inducing a blurred shape with strong quantum coherences in compounds of the lightest elements, H$_2$, D$_2$, T$_2$, and HeH…
Quantum tracking control aims to identify applied fields to steer the expectation values of particular observables along desired paths in time. The associated temporal fields can be identified by inverting the underlying dynamical equations for the observables. However, fields found in this manner are often plagued by undesirable singularities. In this paper we consider a planar molecular rotor, and derive singularity-free tracking expressions for the fields that steer the expectation of the orientation of the rotor along desired trajectories in time. Simulations are presented that utilize two…
In most cases the ultrafast dynamics of resonantly excited molecules are considered, and almost always computed in the molecular frame, while experiments are carried out in the laboratory frame. Here we provide a formalism in terms of a lab frame density matrix which connects quantum dynamics in the molecular frame to those in the laboratory frame, providing a transparent link between computation and measurement. The formalism reveals that in any such experiment, the molecular frame dynamics vary for molecules in different orientations and that certain coherences which are potentially experime…
We present a theoretical study of the shaping of the time-evolution of field-free orientation of linear molecules. We show the extend to which the degree of orientation can be steered along a desired periodic time-dependent signal. The objective of this study is not to optimize molecular orientation but to propose a general procedure to precisely control rotational dynamics through the first moment of the molecular axis distribution. Rectangular and triangular signals are taken as illustrative examples. At zero temperature, we compute the quantum states leading to such field-free dynamics. A T…
We show that combined permanent and induced electric dipole interactions of polar and polarizable molecules with collinear electric fields lead to a sui generis topology of the corresponding Stark energy surfaces and of other observables - such as alignment and orientation cosines - in the plane spanned by the permanent and induced dipole interaction parameters. We find that the loci of the intersections of the surfaces can be traced analytically and that the eigenstates as well as the number of their intersections can be characterized by a single integer index. The value of the index, distinc…
Efficient and long-lived field-free molecular orientation is achieved using only two kicks appropriately delayed in time. The understanding of the mechanism rests upon a molecular target state providing the best efficiency versus persistence compromise. An optimal control scheme is referred to for fixing the free parameters (amplitudes and the time delay between them). The limited number of kicks, the robustness and the transposability to different molecular systems advocate in favor of the process, when considering its experimental feasibility.
We propose a new formulation of optimal and local control algorithms which enforces the constraint of time-integrated zero-area on the control field. The fulfillment of this requirement, crucial in many physical applications, is mathematically implemented by the introduction of a Lagrange multiplier aiming at penalizing the pulse area. This method allows to design a control field with an area as small as possible, while bringing the dynamical system close to the target state. We test the efficiency of this approach on two control purposes in molecular dynamics, namely, orientation and photodis…
We detail and extend the results of [Milman {\it et al.}, Phys. Rev. Lett. {\bf 99}, 130405 (2007)] on Bell-type inequalities based on correlations between measurements of continuous observables performed on trapped molecular systems. We show that for some observables with a continuous spectrum which is bounded, one is able to construct non-locality tests sharing common properties with those for two-level systems. The specific observable studied here is molecular spatial orientation, and it can be experimentally measured for single molecules, as required in our protocol. We also provide some u…
This study shows the unexpected and counter-intuitive possibility of simultaneously orienting a molecule while delocalizing its molecular axis in a plane in field-free conditions. The corresponding quantum states are characterized and different control strategies using shaped THz laser pulses are proposed to reach such states at zero and nonzero temperatures. The robustness against temperature effects of a simple control procedure combining a laser and a THz pulse is shown. Such control strategies can be applied not only to linear molecules but also to symmetric top molecules.
We show that field-free molecular orientation induced by a half-cycle pulse may be considerably enhanced by an additional laser pulse inducing molecular anti-alignment. Two qualitatively different enhancement mechanisms are identified depending on the pulse order, and their effects are optimized with the help of quasi-classical as well as fully quantum models.
We theoretically consider the phenomenon of field-free long-lasting orientation of symmetric-top molecules ionized by two-color laser pulses. The anisotropic ionization produces a significant long-lasting orientation of the surviving neutral molecules. The degree of orientation increases with both the pulse intensity and, counterintuitively, with the rotational temperature. The orientation may be enhanced even further by using multiple delayed two-color pulses. The long-lasting orientation may be probed by even harmonic generation or by Coulomb-explosion-based methods. The effect may enable th…
We present a combined analytical and numerical investigation to show how an optimal control field can be designed to generate maximum field-free orientation of molecules for three populated rotational states. Based on a model involving pure rotational ladder-climbing excitation between rotational states, a set of optimal amplitude and phase conditions are analytically derived for the applied control fields. The maximum degree of orientation can be achieved when the field satisfies amplitude and phase conditions at the two transition frequencies. Multiple optimal solutions exist and to examine …
In the field of molecular electronics, particularly in quantum transport studies, the orientation of molecules plays a crucial role. This orientation, with respect to the electrodes, can be defined through the cavity of ring-shaped monocyclic hydrocarbon molecules. In this manuscript, we unveil the geometrical conformation of these molecules when they are trapped between two atomically sharp electrodes through a combination of dynamic simulations, electronic transport calculations based on density functional theory, and break junction experiments under room conditions. Moreover, we present a n…
We have theoretically investigated the molecular orientation by a asymmetric potential created by the superposition of two-color laser fields. The time-dependent Schrodinger equation is solved numerically for different field parameters. We have shown how enhancement or suppression of the molecular orientation can be manipulated by the laser field parameters, such as time between laser pulses, the different intensity of the pulses, etc.
Organic exciton-photon polariton lasers have recently been shown to be remarkable candidates for the realization of efficient sources of coherent light operating at room temperature. While their thresholds are now comparable with conventional organic photon lasers, tuning of molecular conformation and orientation as a means to further enhance their performance remains largely unexplored. Here, we first report a two-fold reduction in the threshold of a polariton laser based on a high-Q microcavity filled with an active layer of poly(9,9-dioctylfluorene) (PFO) when 15% β-phase conformation is in…
We study Frenkel exciton-polariton Bose-Einstein condensation in a two-dimensional defect-free triangular photonic crystal with an organic semiconductor active medium containing bound excitons with dipole moments oriented perpendicular to the layers. We find photonic Bloch modes of the structure and consider their strong coupling regime with the excitonic component. Using the Gross- Pitaevskii equation for exciton polaritons and the Boltzmann equation for the external exciton reservoir, we demonstrate the formation of condensate at the points in reciprocal space where photon group velocity equ…
Max-Born-Institut（马克斯·博恩研究所）；Insitute of Physics, Humboldt University zu Berlin（柏林洪堡大学物理研究所）；Technion - Israel Institute of Technology（以色列理工学院）；School of Molecular Sciences, Arizona State University（亚利桑那州立大学分子科学学院）；Department of Physics, Imperial College London（伦敦帝国理工学院物理系）；Department of Physics, Freie Universität Berlin（柏林自由大学物理系）；Technische Universität Berlin（柏林工业大学）
Intense terahertz-frequency pulses induce coherent rotational dynamics and orientation of polar molecular ensembles. Exact numerical methods for rotational dynamics are computationally not feasible for the vast majority of molecular rotors - the asymmetric top molecules at ambient temperatures. We exemplify the use of Random Phase Wave Functions (RPWF) by calculating the terahertz-induced rotational dynamics of sulfur dioxide (SO2) at ambient temperatures and high field strengths and show that the RPWF method gains efficiency with the increase in temperature and in the THz-field strengths. The…
We present a combined analytical and numerical study for coherent terahertz control of a single molecular polariton, formed by strongly coupling two rotational states of a molecule with a single-mode cavity. Compared to the bare molecules driven by a single terahertz pulse, the presence of a cavity strongly modifies the post-pulse orientation of the polariton, making it difficult to obtain its maximal degree of orientation. To solve this challenging problem toward achieving complete quantum coherent control, we derive an analytical solution of a pulse-driven quantum Jaynes-Cummings model by ex…
