Quantum entanglement and coherence are both essential physical resources in quantum theory. Cold polar molecules have long coherence time and strong dipole-dipole interaction and thus have been suggested as a platform for quantum information processing. In this paper, we employ the pendular states of the polar molecules trapped in static electric fields as the qubits, and put forward several theoretical schemes to generate the entanglement and coherence for two coupled dipoles by using optimal control theory. Through the designs of appropriate laser pulses, the transitions from the ground state to the Bell state and maximally coherent state can be realized with high fidelities 0.9906 and 0.9943 in the two-dipole system, respectively. Meanwhile, we show that the degrees of entanglement and coherence between the two pendular qubits are effectively enhanced with the help of optimized control fields. Furthermore, our schemes are generalized to the preparation of the Hardy state and even to the creation of arbitrary two-qubit states. Our findings can shed some light on the implementation of quantum information tasks with the molecular pendular states.
We investigate the entanglement between electronic and vibrational degrees of freedom produced by a vibronic coupling in a molecular system described in the Born-Oppenheimer approximation. Entanglement in a pure state of the Hilbert space
H=Hel⨂Hvib is quantified using the von Neumann entropy of the reduced density matrix and the reduced linear entropy. Expressions for these entanglement measures are derived for the $2\ifmmode\times\else\texttimes\fi{}{N}_{v}$ and $3\ifmmode\times\else\texttimes\fi{}{N}_{v}$ cases of the bipartite entanglement, where 2 and 3 are the dimensions of the electronic Hilbert space
Hel, and
Nv is the dimension of
Hvib. We study the entanglement dynamics for two electronic states coupled by a laser pulse (a $2\ifmmode\times\else\texttimes\fi{}{N}_{v}$ case), taking as an example a coupling between the ${a}^{3}{{\ensuremath{\Sigma}}_{u}}^{+}(6s,6s)$ and
1g(6s,6p3/2) states of the Cs
2 molecule. The reduced linear entropy expression obtained for the $3\ifmmode\times\else\texttimes\fi{}{N}_{v}$ case is used to follow the entanglement evolution in a scheme proposed for the control of the vibronic dynamics in a Cs
2 cold molecule, implying the ${a}^{3}{{\ensuremath{\Sigma}}_{u}}^{+}(6s,6s)$, ${0}_{g}{}^{\ensuremath{-}}(6s,6{p}_{3/2})$, and ${0}_{g}{}^{\ensuremath{-}}(6s,5d)$ electronic states, which are coupled by a nonadiabatic radial coupling and a sequence of chirped laser pulses.
We propose an alternative scenario for the generation of entanglement between rotational quantum states of two polar molecules. This entanglement arises from dipole-dipole interaction, and is controlled by a sequence of laser pulses simultaneously exciting both molecules. We study the efficiency of the process, and discuss possible experimental implementations with cold molecules trapped in optical lattices or in solid matrices. Finally, various entanglement detection procedures are presented, and their suitability for these two physical situations is analyzed.
While many-particle entanglement can be found in natural solids and strongly interacting atomic and molecular gases, generating highly entangled states between weakly interacting particles in a controlled and scalable way presents a significant challenge. We describe here a one-step method to generate entanglement in a dilute gas of cold polar molecules. For molecules in optical traps separated by a few micrometers, we show that maximally entangled states can be created using the strong off-resonant pulses that are routinely used in molecular alignment experiments. We show that the resulting alignment-mediated entanglement can be detected by measuring laser-induced fluorescence with single-site resolution and that signatures of this molecular entanglement also appear in the microwave absorption spectra of the molecular ensemble. We analyze the robustness of these entangled molecular states with respect to intensity fluctuations of the trapping laser and discuss possible applications of the system for quantum information processing.
We present an experimental and theoretical investigation of the quantum control of ground-state rotational coherence in a linear molecule. A sequence of two temporally separated laser pulses creates a rotational superposition state in
CO2 whose evolution is monitored through a polarization technique. We study the influence of the phase difference between the two pulses. We show that the overlapping of the two wave packets, produced by each pulse, gives rise to quantum interference that affects the orientational anisotropy of the sample. Because of the large number of coherently excited levels, the interference produces well-separated temporal structures, whose magnitude can be controlled through the relative delay of the two pulses.