Orientations of two coupled molecules

Abstract

Orientation states of two coupled polar molecules controlled by laser pulses are studied theoretically. By varying the period of a series of periodically applied laser pulse, transition from regular to chaotic behavior may occur. Schmidt decomposition is used to measure the degree of entanglement. It is found that the entanglement can be enhanced by increasing the strength of laser pulse.PACS [5,6]. Experimentally, several methods have been used to control the orientations of molecules [7,8,9,10,11]. For example, by turning on a picosecond laser pulse adiabatically, the pendular stateshybrid of field-free molecular eigenstates [12,13,14] -can be created. A femtosecond laser pulse, like impulsive excitation, is found to be able to generate a field-free orientation [15,16].Since entangled states are fundamental for quantum information processing [17,18], many research works have been proposed to generate entanglement in quantumoptic and atomic systems [19,20]. In this Letter we propose a novel way to generate entanglement between two coupled identical polar molecules separated in a distance of tens of nanometers. Both molecules are irradiated by ultra-short pulses of laser light. Our study shows the entanglement induced by the dipole interaction can be enhanced by controlling the inter-molecule distance and the field strength of laser pulse.Consider now two identical polar molecules (separated by a distance of R ). There exists dipole-dipole interaction between these two molecules. Ultrashort halfcycle laser pulses are applied to both molecules [21]. The Hamiltonian of the system can be written aswhere L 2 j andh 2 2I (= B) are the angular momentum operator and rotational constant, respectively./R 3 is the dipole interaction between two molecules, where µ 1 and µ 2 are the dipole moments. For simplicity, the dipole moments of two molecules are assumed to be identical, i.e. µ 1 = µ 2 = µ. The field-molecule coupling can be expressed as H l = −µE (t) cos θ cos (ωt) − µE (t) cos θ ′ cos (ωt) ,where θ and θ ′ are the angles between the dipole moments and laser field. The laser profile is assumed to be Gaussian shape, i.e. E (t) = E 0 e − (t−to) 2 σ 2, where E 0 is the field strength, t 0 is the center of peak, and σ is the pulse duration. With these assumptions, the time-dependent Schrödinger equation can be solved by expanding the wave function in terms of a series of field-free spherical harmonic functions (2) where (θ, φ) and θ ′ , φ ′ are the coordinates of first and second molecule respectively. c lml ′ m ′ (t) are the timedependent coefficients corresponding to the quantum numbers (l, m; l ′ , m ′ ) and can be determined by solving the Schrödinger equations numerically. In above equation, total wavefunction has no spatial dependence since we keep inter-molecule separation R as a fixed parameter. One might argue that variation of R is inevitable because of the effects of laser fields or inter-molecule vibrations. However, recent experiments have shown that it is possible to resolve two individual molecules separ...

Molecular orientation entanglement and temporal Bell-type inequalities

“…From the experimental point of view, motivations for this work are the recent advances in single molecule manipulation and detection with entanglement creation [13] and quantum information purposes [14,16,17,18]. In particular, trapped cold polar molecules are promissing candidates for quantum information processing based on the manipulation of their rotational levels [27].…”

Orientation of adsorbed dipolar molecules: A conical well model

“…In particular, a molecular system evolves from a nonentangled case to an entangled one. According to our previous study, 17 it is found that the orientations of the coupled rotors relate closely to the entropy. This means that the orientations of the coupled rotors somehow reflect the entropy of the system and thus relates to the measurement of the entanglement.…”

“…14 Recently, great attention has been focused on the coupledrotor system since peculiar behaviors may occur in the presence of dipole-dipole interaction. [15][16][17] For example, recent neutron scattering experiments on certain Hofmann clathrates have reported the temperature-dependent behavior of the linewidths. 18 A line broadening mechanism based on rotor-rotor coupling was proposed for the explanation of the widths.…”

Polarization entanglement of sum-frequency photons: A tool to probe the Markovian limit

“…In principle, this provides a 2 N capacity to store information [5]. Quantum computing stimulates the development of silicon chip technology [6][7][8], the ion trap technique [9], and the engineering of rotational [10][11][12] and/or vibrational packets [13,14]. Furthermore, progress in the preparation of entangled photons [15,16] has stimulated interest in using them as a spectroscopic tool.…”