Recently, it was predicted theoretically and verified experimentally that a pair of delayed and cross-polarized short laser pulses can create molecular ensembles with a well defined sense of rotation (clockwise or counterclockwise). Here we provide a comparative study of the classical and quantum aspects of the underlying mechanism for linear molecules and for symmetric tops, like benzene molecules, that were used for the first experimental demonstration of the effect. Very good quantitative agreement is found between the classical description of the process and the rigorous quantum mechanical analysis at the relevant experimental conditions. Both approaches predict the same optimal values for the delay between pulses and the angle between them, and deliver the same magnitude of the induced oriented angular momentum of the molecular ensemble. As expected, quantum and classical analysis substantially deviate when the delay between pulses is comparable with the period of quantum rotational revivals. However, time-averaged characteristics of the excited molecular ensemble are equally good described by the these two approaches. This is illustrated by calculating the anisotropic time-averaged angular distribution of the double-pulse excited molecules, which reflects persistent confinement of the molecular axes to the rotation plane defined by two polarization vectors of the pulses.
We introduce a new scheme for controlling the sense of molecular rotation. By varying the polarization and the delay between two ultrashort laser pulses, we induce unidirectional molecular rotation, thereby forcing the molecules to rotate clockwise/counterclockwise under field-free conditions. We show that unidirectionally rotating molecules are confined to the plane defined by the two polarization vectors of the pulses, which leads to a permanent anisotropy in the molecular angular distribution. The latter may be useful for controlling collisional cross-sections and optical and kinetic proces…
An isotropic medium, having magnetic sublevels, when subjected to a magnetic field or an electromagnetic field can induce anisotropy in the medium; and as a result the plane of polarization of the probe field can rotate. Therefore the rotation due to the magnetic field alone, can be {\em controlled efficiently} with use of a coherent field. We show, using a control field, significant enhancement of the magneto-optical rotation and demonstrate the possibility of realizing {\em magneto-optical switch}.
Semiclassical catastrophes in the dynamics of a quantum rotor (molecule) driven by a strong time-varying field are considered. We show that for strong enough fields, a sharp peak in the rotor angular distribution can be achieved via time-domain focusing phenomenon, followed by the formation of angular rainbows and glory-like angular structures. Several scenarios leading to the enhanced angular squeezing are proposed that use specially designed and optimized sequences of pulses. The predicted effects can be observed in many processes, ranging from molecular alignment (orientation) by laser fiel…
We demonstrate coherent control of both the rotational and hyperfine state of ultracold, chemically stable $^{87}$Rb$^{133}$Cs molecules with external microwave fields. We create a sample of ~2000 molecules in the lowest hyperfine level of the rovibronic ground state N = 0. We measure the transition frequencies to 8 different hyperfine levels of the N = 1 state at two magnetic fields ~23 G apart. We determine accurate values of rotational and hyperfine coupling constants that agree well with previous calculations. We observe Rabi oscillations on each transition, allowing complete population tr…
We report on the possibility of controlling quantum random walks with a step-dependent coin. The coin is characterized by a (single) rotation angle. Considering different rotation angles, one can find diverse probability distributions for this walk including: complete localization, Gaussian and asymmetric likes. In addition, we explore the entropy of walk in two contexts; for probability density distributions over position space and walker's internal degrees of freedom space (coin space). We show that entropy of position space can decrease for a step-dependent coin with the step-number, quite …
Photonic topological insulator plates violate Lorentz reciprocity which leads to a directionality of surface-guided modes. This in-plane directionality can be imprinted via an applied magnetic field. On the basis of macroscopic quantum electrodynamics in nonreciprocal media, we show that two photonic topological insulator surfaces are subject to a tuneable, magnetic-field dependent Casimir torque. Due to the directionality, this torque exhibits a unique $2π$ periodicity, in contradistinction to the Casimir torques encountered for reciprocal uniaxial birefringent media or corrugated surfaces wh…
Laser control of molecular rotation is an area of active research. A number of recent studies has aimed at expanding the reach of rotational control to extreme, previously inaccessible rotational states, as well as controlling the directionality of molecular rotation. Dense ensembles of molecules undergoing ultrafast uni-directional rotation, known as molecular superrotors, are anticipated to exhibit unique properties, from spatially anisotropic diffusion and vortex formation to the creation of powerful acoustic waves and tuneable THz radiation. Here we describe our recent progress in controll…
We consider deflection of polarizable molecules by inhomogeneous optical fields, and analyze the role of molecular orientation and rotation in the scattering process. It is shown that molecular rotation induces spectacular rainbow-like features in the distribution of the scattering angle. Moreover, by preshaping molecular angular distribution with the help of short and strong femtosecond laser pulses, one may efficiently control the scattering process, manipulate the average deflection angle and its distribution, and reduce substantially the angular dispersion of the deflected molecules. We pr…
Sagnac interferometers with massive particles promise unique advantages in achieving high precision measurements of rotation rates over their optical counterparts. Recent proposals and experiments are exploring non-ballistic Sagnac interferometers where trapped atoms are transported along a closed path. This is achieved by using superpositions of internal quantum states and their control with state-dependent potentials. We address emergent questions regarding the dynamical behavior of Bose-Einstein condensates in such an interferometer and its impact on rotation sensitivity. We investigate com…
Randomness has attracted great interest in the field of music composition for quite some time. As early as 1962, Iannis Xenakis started exploring a stochastic approach to randomness by using computer-based interlinking probability functions to determine compositional structure, pitches and their durations. Soon after, composers and music technologists started to explore randomness with various methods of algorithmic compositions, sometimes with the help of artificial intelligence. However, in most cases, the source of randomness they used was in fact deterministic in nature. That is to say, th…
In the framework of optical quantum computing and communications, a major objective consists in building receiving nodes that implement conditional operations on incoming photons, using the interaction with a single stationary qubit. In particular, the quest for scalable nodes motivated the development of cavity-enhanced spin-photon interfaces with solid-state emitters. An important challenge remains, however, to produce a stable, controllable, spin-dependant photon state, in a deterministic way. Here we use a pillar-based high-Q cavity, embedding a singly-charged semiconductor quantum dot, to…
Controlling the internal degrees of freedom is a key challenge for applications of cold and ultracold molecules. Here, we demonstrate rotational-state cooling of trapped methyl fluoride molecules (CH3F) by optically pumping the population of 16 M-sublevels in the rotational states J=3,4,5, and 6 into a single level. By combining rotational-state cooling with motional cooling, we increase the relative number of molecules in the state J=4, K=3, M=4 from a few percent to over 70%, thereby generating a translationally cold (~30mK) and nearly pure state ensemble of about 10^6 molecules. Our scheme …
It was shown by M.A. Nielsen and I.L. Chuang 1997, that it is impossible to build strictly universal programmable quantum gate array, that could perform any unitary operation precisely and it was suggested to use probabilistic gate arrays instead. In present work is shown, that if to use more physical and weak condition of universality (suggested already in earliest work by D.Deutsch 1985) and to talk about simulation with arbitrary, but finite precision, then it is possible to build universal programmable gate array. But now the same no-go theorem by Nielsen and Chuang will have new interesti…
We show that detuned optical pulse trains with a modest spectral width can polarize nuclear spins in InAs quantum dots. The pulse bandwidth is large enough to excite a coherent superposition of both electron spin eigenstates in these negatively charged dots but narrow enough to give partial spectral selectivity between the eigenstates. The coherent precession of electron spin states and periodic excitation focuses the nuclear spin distribution, producing a discrete set of precession modes. The spectral selectivity generates a net nuclear polarization, through a mechanism that relies on optical…
This study proposes a pioneering protocol for teleporting an arbitrary single particle state and simultaneously performing a rotation operation on that particle. There are protocols for either only teleporting particles or only remotely controlling quantum particles. If one has to remotely control a teleported quantum, then he/she has to first do the quantum teleportation and then perform the remote control on the teleported quantum. Both operations were done separately on two sets of entanglements. However, this intuitive solution is inefficient because many resources are wasted. Therefore, t…
By applying a circularly polarized and slightly blue-detuned microwave field with respect to the first excited rotational state of a dipolar molecule, one can engineer a long-range, shallow potential well in the entrance channel of the two colliding partners. As the applied microwave ac-field is increased, the long-range well becomes deeper and can support a certain numbers of bound states, which in turn bring the value of the molecule-molecule scattering length from a large negative value to a large positive one. We adopt an adimensional approach where the molecules are described by a rescale…
We investigate theoretically the interaction of polar molecules with optical lattices and microwave fields. We demonstrate the existence of frequency windows in the optical domain where the complex internal structure of the molecule does not influence the trapping potential of the lattice. In such frequency windows the Franck-Condon factors are so small that near-resonant interaction of vibrational levels of the molecule with the lattice fields have a negligible contribution to the polarizability and light-induced decoherences are kept to a minimum. In addition, we show that microwave fields c…
Ultracold molecules trapped in optical tweezers show great promise for the implementation of quantum technologies and precision measurements. We study a prototypical scenario where two interacting polar molecules placed in separate traps are controlled using an external electric field. This, for instance, enables a quantum computing scheme in which the rotational structure is used to encode the qubit states. We estimate the typical operation timescales needed for state engineering to be in the range of few microseconds. We further underline the important role of the spatial structure of the tw…
Quantum circuit model is the most popular paradigm for implementing complex quantum computation. Based on Cartan decomposition, we show that $2(N-1)$ generalized controlled-$X$ (GCX) gates, $6$ single-qubit rotations about the $y$- and $z$-axes, and $N+5$ single-partite $y$- and $z$-rotation-types which are defined in this paper are sufficient to simulate a controlled-unitary gate $\mathcal{U}_{cu(2\otimes N)}$ with $A$ controlling on $\mathbb{C}^2\otimes \mathbb{C}^N$. In the scenario of the unitary gate $\mathcal{U}_{cd(M\otimes N)}$ with $M\geq3$ that is locally equivalent to a diagonal uni…
In a recent work, we have shown that all solutions to the Weyl equation and a special class of solutions to the Dirac equation are degenerate in the sense that they remain unaltered under the influence of a wide variety of different electromagnetic fields. In this study, our previous work is significantly extended, providing a wide class of degenerate solutions to the Dirac equation for massless particles. The electromagnetic fields corresponding to these solutions are calculated and examples regarding both spatially constant electromagnetic fields and electromagnetic waves are also provided. …
We present an analysis of two experimental approaches to controlling the directionality of molecular rotation with ultrashort laser pulses. The two methods are based on the molecular interaction with either a pair of pulses (a "double kick" scheme) or a longer pulse sequence (a "chiral pulse train" scheme). In both cases, rotational control is achieved by varying the polarization of and the time delay between the consecutive laser pulses. Using the technique of polarization sensitive resonance-enhanced multi-photon ionization, we show that both methods produce significant rotational directiona…
We report an experimental and theoretical study of the evolution of vibrational coherence in a thermal ensemble of nitrogen molecules. Rotational dephasing and rephasing of the vibrational coherence is detected by coherent anti-Stokes Raman scattering. The existence of ro-vibrational coupling and the discrete energy spectrum of the rotational bath lead to a whole new class of full and fractional ro-vibrational revivals. Following the rich ro-vibrational dynamics on a nanosecond time scale with sub-picosecond time resolution enables us to determine the second-order ro-vibrational constant $gamm…
We generalize the formulation of non-commutative quantum mechanics to three dimensional non-commutative space. Particular attention is paid to the identification of the quantum Hilbert space in which the physical states of the system are to be represented, the construction of the representation of the rotation group on this space, the deformation of the Leibnitz rule accompanying this representation and the implied necessity of deforming the co-product to restore the rotation symmetry automorphism. This also implies the breaking of rotational invariance on the level of the Schroedinger action …
