# Quantum Optics and Quantum Information -Theory

**Theory**

**High-Fidelity entanglement
via Molecular Dissociation in Integrated Atom Optics**

High-fidelity entanglement of neutral cold atoms can be achieved by combining several already available techniques such as the creation or dissociation of neutral diatomic molecules, manipulating atoms with microfabricated structures (atom chips), and detecting single atoms with almost 100% efficiency. The fidelity of the resulting entanglement is robust against the details of dissociation process. Manipulating this entanglement with integrated or linear atom optics will open a perspective for quantum-information processing with neutral atoms. Details are in the reference below.

Reference:

High-fidelity entanglement
via molecular dissociation in integrated atom optics

Phys. Rev. A 75, 042312 (2007).

**R****obust
creation of entanglement between remote memory qubits**

Duan et al. (DLCZ) proposed a quantum repeater with atomic ensembles and linear optics [1]. The entanglement generation and entanglement swapping depend on single photon Mach-Zehnder-type interference. Consequently the relative phase between the two pairs of entangled state is sensitive to path length fluctuation on the order of sub wavelength of photons. The entanglement generation process is probabilistic, so the path length instability has to be stabilized during the whole process. This is extremely difficult for current techniques.

The well known Hong-Ou-Mandel (HOM) interference requests the path length instability on the order of coherence length of the photons. For the photons created from atomic ensembles with coherence length around 30 m, the Hong-Ou-Mandel-type interference requests the two photon wave packets overlap very well, e.g., 10% delay is acceptable. Therefore the robustness is improved about 7 orders of magnitude higher in comparison with the single-photon Mach-Zehnder-type interference.

Unfortunately, a simple extension of DLCZ protocol using HOM interference doesnˇŻt work. The two-photon state generated in the second-order Spontaneous Raman process will also induce a coincidence count on the detectors. Thus one can only acquire a complex superposition state by performing the Bell-state measurement.

However, by appropriate
designing the Bell state measurement in entanglement swapping, the unwanted
two-excitation terms can be automatically washed out. Ideally, a maximally
entangled pair is created between communication sites A and D after entanglement
swapping. The communication length can be extended by further entanglement
swapping.

Our protocol also allows linear-optical entanglement purification. The photons in mode b1 and b2 are detected in |+/-> basis . The entangled photons of higher fidelity in mode a1 and a2 are restored in atomic ensembles via dark-state-polariton for further manipulation.

Taking into account the imperfections, we will obtain an effective entangled pair between the remote memory qubits. The total time needed scales polynomially or quadratically with the communication length

Reference:

Robust creation of entanglement
between remote atomic ensembles. Phys. Rev. Lett. 98, 240502 (2007).

Fault-tolerant quantum
repeater with atomic ensembles and linear optics. Phys. Rev. A. 76, 022329
(2007).