Molecular Rotational States Research Articles

Dipolar spin-exchange and entanglement between molecules in an optical tweezer array

Ultracold polar molecules are promising candidate qubits for quantum computing and quantum simulations. Their long-lived molecular rotational states form robust qubits, and the long-range dipolar interaction between molecules provides quantum entanglement. In this work, we demonstrate dipolar spin-exchange interactions between single calcium monofluoride (CaF) molecules trapped in an optical tweezer array. We realized the spin- 1 2 quantum XY model by encoding an effective spin- 1 2 system into the rotational states of the molecules and used it to generate a Bell state through an iSWAP operation. Conditioned on the verified existence of molecules in both tweezers at the end of the measurement, we obtained a Bell state fidelity of 0.89(6). Using interleaved tweezer arrays, we demonstrate single-site molecular addressability.

Resonant and non-resonant optimizations by multi-constraint quantum control theory in molecular rotational states

It is a promising research for optimization of quantum gate in the field of quantum computation. We investigate the feasibility of implementing the single-qubit gate (Hadamard) in molecular rotational system. By applying the Multi-constraint quantum optimal control method, the excepted final states can be achieved based on the molecular rotational states both in resonant and non-resonant cases with the control pulses. The permanent electric dipole moment is ignored in non-resonance. Besides, the zero-pulse area constraint and the constant fluence constraint are employed to optimize shapes of control pulses. Finally, we show that the Hadamard gate can be realized with the high fidelity (0.9999) and also examine the dependence of the fidelity on pulse fluence as well as the control pulse.

On the use of stereodynamical effects to control cold chemical reactions: The H + D2 ⟷ D + HD case study.

Quantum calculations are reported for the stereodynamic control of the H + D2 ↔ D + HD chemical reaction in the energy range of 1-50K. Stereodynamic control is achieved by a formalism similar to that reported by Perreault et al. [Nat. Chem. 10, 561 (2018)] in recent experimental works in which the alignment of the molecular bond axis relative to the incident relative velocity is controlled by selective preparations of the molecule in a specific or superposition of magnetic projection quantum numbers of the initial molecular rotational level. The approach presented here generalizes the experimental scheme of Perreault et al. and offers additional degree of control through various experimental preparations of the molecular alignment angle. Illustrative results presented for the H + D2 and D + HD reactions show significant control with the possibility of turning the reaction completely on or off with the appropriate stereodynamic preparation of the molecular state. Various scenarios for maximizing and minimizing the reaction outcomes are identified with the selective preparation of molecular rotational states.

Discrimination of enantiomers through quantum interference and quantum Zeno effect.

Quantum optical methods have great potential for highly efficient discrimination of chiral molecules. We propose quantum interference-based schemes of enantio-discrimination under microwave regime among molecular rotational states. The quantum interference between field-driven one- and two-photon transitions of two higher states is designed to be constructive for one enantiomer but destructive for the other, since a certain transition dipole moment can be set to change sign with enantiomers. Therefore, two enantiomers can evolve into entirely different states from the same ground state. Through strengthening the constructive interference, the quantum Zeno effect is found in one enantiomer and then its excitation is suppressed, which also enables the enantio-discrimination. We simulate the schemes for differentiating between S and R enantiomers of 1, 2-propanediol (C3H8O2) molecules. With the analysis of the phase sensitivity to microwave fields and the effect of energy relaxations, the highly efficient enantio-discrimination of the 1, 2-propanediol molecules may be achieved.

Nondestructive dispersive imaging of rotationally excited ultracold molecules.

A barrier to realizing the potential of molecules for quantum information science applications is a lack of high-fidelity, single-molecule imaging techniques. Here, we present and theoretically analyze a general scheme for dispersive imaging of electronic ground-state molecules. Our technique relies on the intrinsic anisotropy of excited molecular rotational states to generate optical birefringence, which can be detected through polarization rotation of an off-resonant probe laser beam. Using 23Na87Rb and 87Rb133Cs as examples, we construct a formalism for choosing the molecular state to be imaged and the excited electronic states involved in off-resonant coupling. Our proposal establishes the relevant parameters for achieving degree-level polarization rotations for bulk molecular gases, thus enabling high-fidelity nondestructive imaging. We additionally outline requirements for the high-fidelity imaging of individually trapped molecules.

Creation of vibrationally-excited ultralong-range Rydberg molecules in polarized and unpolarized cold gases of 87Sr

Photoexcitation rates for creation of ultralong-range Rydberg molecules with 31 ≲ n ≲ 41 in both ground and excited vibrational levels in cold (T ∼ 900 nK) gases of polarized and unpolarized 87Sr are presented. The measured production rates of the ν = 0, 1 and 2 vibrational levels reveal rather different n dependences which are analyzed by evaluating the Franck–Condon factors associated with excitation of the different vibrational levels and molecular rotational states. In particular, for gases of spin-polarized fermions, only Rydberg dimers with odd rotational quantum numbers are excited due to the requirement that their wave functions be anti-symmetric with respect to exchange. The data also demonstrate that measurements of the formation of vibrationally-excited ν = 1 molecules can furnish a probe of pair correlations over intermediate length scales.

Interference effects due to nuclear motion of the hydrogen molecule

We show that two-particle interferences can be used to probe the nuclear motion in a doubly excited hydrogen molecule. The dissociation of molecular hydrogen by electron impact involves several decay channels, associated with different molecular rotational states, which produce quantum interferences in the detection of the atomic fragments. Thanks to the correlations between the angular momentum and the vibrational states of the molecule, the fragments arising from each dissociation channel carry out a phase shift which is a signature of the molecule rotation. These phase shifts, which cannot be observed in a single-atom detection scheme, may be witnessed under realistic experimental conditions in a time-of-flight coincidence measurement. We analyze the interferences arising from the two lowest-energy rotational states of a parahydrogen molecule. Our result shows the relevance of two-fragment correlations to track the molecular rotation.

Controlling population of the molecular rotational state and the alignment theoretically by tailored femtosecond laser pulse.

We demonstrate that the population of the molecular rotational state through a stimulated impulsive Raman excitation can be controlled by tailoring the femtosecond laser pulse with a V-style phase modulation. The results show that, by precisely manipulating the modulation parameters, both the odd and even populations of the molecular rotational state can be completely suppressed or reconstructed. Meanwhile, the relative excitation between the odd and even populations can be obtained. Finally, we show that field-free molecular alignment can be controlled due to the modulation of the molecular rotational state populations.

Rydberg-atom-mediated nondestructive readout of collective rotational states in polar-molecule arrays

We analyze in detail the possibility to use charge-dipole interaction between a single polar molecule or a 1D molecular array and a single Rydberg atom to read out rotational populations. The change in the Rydberg electron energy is conditioned on the rotational state of the polar molecules, allowing for realization of a CNOT quantum gate between the molecules and the atom. Subsequent readout of the atomic fluorescence results in a non-destructive measurement of the rotational state. We study the interaction between a 1D array of polar molecules and an array or a cloud of atoms in a Rydberg superatom (blockaded) state and calculate the resolved energy shifts of Rb(60s) with KRb and RbYb molecules, with N=1, 3, 5 molecules. We show that collective molecular rotational states can be read out using the conditioned Rydberg energy shifts.

Rotational-State-Dependent Dispersion of Molecules by Pulsed Optical Standing Waves.

We report on the rotational-state-dependent, transverse acceleration of CS_{2} molecules affected by pulsed optical standing waves. The steep gradient of the standing wave potential imparts far stronger dipole forces on the molecules than propagating pulses do. Moreover, large changes in the transverse velocities (i.e., up to 80 m/s) obtained with the standing waves are well reproduced in numerical simulations using the effective polarizability that depends on the molecular rotational states. Our analysis based on the rotational-state-dependent effective polarizability can therefore serve as a basis for developing a new technique of state selection for both polar and nonpolar molecules.

Hindered rotational physisorption states of H2 on Ag(111) surfaces.

We have investigated the physisorption states of H2 on Ag(111) surfaces. To clarify the accurate adsorption properties of H2 on Ag(111), we performed first-principles calculations based on spin-polarized density functional theory (DFT) with the semiempirical DFT-D2 method and the newly-developed exchange functional with the non-local correlation functional vdW-DF2 (rev-vdW-DF2). We constructed exhaustive potential energy surfaces, and revealed that non-negligible out-of-plane potential anisotropy with a perpendicular orientation preference exists even for H2 physisorption on planar Ag(111), as predicted by previous results of resonance-enhanced multiphoton ionization spectroscopy and temperature-programmed desorption experiments. Therefore, the molecular rotational ground states of ortho-H2 split into two energy levels in the anisotropic potential. The obtained adsorption energy and the number of bound states, including the zero-point energies and the rotational energy shift, agree with diffractive and rotationally mediated selective adsorption scattering resonance measurements. The origin of the potential anisotropy on Ag(111) is a combination of the London dispersion interaction and the virtual transition of the metal electron to the unoccupied molecular state.

Distribution of xp in some molecular rotational states

Developing the analysis of the distribution of the so-called posmom xp to the spherical harmonics that represents some molecular rotational states for such as diatomic molecules and spherical cage molecules, we obtain posmometry (introduced recently by Y. A. Bernard and P. M. W. Gill, Posmom: The Unobserved Observable, J. Phys. Chem. Lett. 1(2010)1254) of the spherical harmonics and demonstrate that it bears a striking resemblance to the momentum distributions of the stationary states for a one-dimensional simple harmonic oscillator.

Simultaneous detection of Raman- and collision-induced molecular rotations of O2 and N2 via femtosecond multi-pulses in combination with quartz-enhanced photoacoustic spectroscopy

Molecular rotational states of nitrogen and oxygen molecules at room temperature and atmospheric pressure are excited by femtosecond double- and multi-pulses with variable temporal pulse distances, and quartz-enhanced photoacoustic spectroscopy is used for their detection. A simple extrapolation of measured double-pulse data is presented, which predicts form and position of Raman-excited spectral features and thus enables us to distinguish between spectral lines caused by Raman-scattering- and collision-induced absorption both appearing when excitation by pulse trains is used.

Non-adiabatic rotational excitation of dipolar molecule under the influence of delayed pulses

We suggest a control scheme for choosing populations of molecular rotational states by wave packet interference. The rotational wave packets of LiCl molecule excited non-adiabatically by half cycle pulse (HCP) is controlled using the second ultrashort HCP. By adjusting the time delay between the two laser pulses, constructive or destructive interference among these wave packets enables the population to be enhanced or repressed for the specific rotational state. The role played by the field strength and the pulse duration is also calculated numerically. We have used fourth order Runge–Kutta method to study non-adiabatic rotational excitation (NAREX) dynamics.

Role of rotational state-selected for nonadiabatic alignment: OCS molecules in femtosecond laser fields

Nonadiabatic alignment by intense nonresonant laser fields is a versatile technique to manipulate the spatial direction of molecules. By solving the time-dependent Schrodinger equation numerically the degree of alignment of the molecules initially in different rotational state are calculated and the results show that the degree of alignment strongly depends on the initial rotational state. Thus, the present study indicates that, for obtaining a high degree of alignment for molecules, appropriate selection of molecular rotational states is necessary.

Quantum phase analysis of field-free molecular alignment

We present quantum mechanical explanations for unresolved phenomena observed in field-free molecular alignment by a femtosecond laser pulse. Quantum phase analysis of molecular rotational states reveals the physical origin of the following phenomena: strong alignment peaks appear periodically, and the temporal shape of each alignment peak changes in an orderly fashion depending on molecular species; the strongest alignment is not achieved at the first peak; the transition between aligned and antialigned states is very fast compared to the time scale of rotational dynamics. These features are understood in a unified way analogous to that describing a carrier-envelope-phase-stabilized mode-locked laser.

Controlling rotational dynamics and alignment of molecule by infrared laser pulse

We investigate the effects of delayed infrared laser (IRL) pulse shape on the non-adiabatic rotational excitation and alignment of a polar molecule. We suggest a control scheme for choosing populations of molecular rotational states by wave packet interference. The rotational wave packets of polar molecule (here HBr) excited non-adiabatically by orienting pulse is controlled actually using the second delayed IRL pulse. By adjusting the time delay between the two laser pulses and the shape of delayed IRL pulse, constructive or destructive interference among these wave packets enables the population to be enhanced or repressed for the specific rotational state. We have used fourth order Runge–Kutta method to study the non-adiabatic rotational excitation (NAREX) dynamics.

Manipulation of molecular rotational dynamics with multiple laser pulses

In this paper, a theoretical model is proposed to investigate the molecular rotational state populations pumped by multiple laser pulses through an impulsive Raman process based on second-order perturbation theory and an analytical solution for the dependence of the rotational state populations on the time delays and the relative amplitudes of the multiple laser pulses has been achieved. The results indicate that the molecular rotational state populations can be controlled by precisely manipulating the time delays and the relative amplitudes, which can be significantly enhanced or completely suppressed, and so the molecular rotational wave packet and field-free molecular alignment can be efficiently manipulated.

Coherent control of molecular rotational state populations by periodic phase-step modulation

We theoretically demonstrate that the molecular rotational state populations through an impulsive nonresonant Raman process can be manipulated by shaping the femtosecond laser pulse with a periodic phase-step modulation. We show that, by precisely controlling these parameters characterizing the periodic phase-step modulation, both the odd and even rotational state populations can be completely suppressed or reconstructed as that induced by the transform-limited laser pulse, and the relative excitation between the odd and even rotational state populations can also be obtained. Furthermore, we show that the field-free molecular alignment can be manipulated due to the modulation of the odd and even rotational state populations.

Controlling molecular rotational population by wave-packet interference

We propose a control scheme for selecting populations of molecular rotational states by wave-packet interference. A series of coherent rotational wave packets is created by nonadiabatic rotational excitation of molecules using two strong femtosecond laser pulses. By adjusting the time delay between the two laser pulses, constructive or destructive interference among these wave packets enables the population to be enhanced or suppressed for a specific rotational state. The evolution of the rotational wave packet with selected populations produces interference patterns with controlled spatial symmetries. This method provides an approach to prepare a molecular ensemble with selected quantum-state distributions and controlled spatial distributions under field-free condition.