We analyze multipartite entanglement between atomic ensembles within quantum matter–light interfaces. In our proposal, a polarized light beam crosses sequentially several polarized atomic ensembles impinging on each of them at a given angle α i . These angles are crucial parameters for shaping the entanglement since they are directly connected to the appropriate combinations of the collective atomic spins that are squeezed. We exploit such a scheme to go beyond the pure state paradigm proposing realistic experimental settings to address multipartite mixed state entanglement in continuous variables.
We analyze multipartite entanglement between atomic ensembles within quantum matter–light interfaces. In our proposal, a polarized light beam crosses sequentially several polarized atomic ensembles impinging on each of them at a given angle α i . These angles are crucial parameters for shaping the entanglement since they are directly connected to the appropriate combinations of the collective atomic spins that are squeezed. We exploit such a scheme to go beyond the pure state paradigm proposing realistic experimental settings to address multipartite mixed state entanglement in continuous variables.
Summary form only given. A new approach to the problem of the quantum interface between light and atoms has been recently developed. The method utilizes free space dispersive interaction between pulses of light and spin polarized atomic ensembles. Entanglement between the polarization state of light and the collective spin state of atoms is established by measurement, more precisely by detection of light in a certain polarization basis. In the first demonstration of this approach we have generated a long-lived entangled state of two separate macroscopic atomic samples by a polarization measurement on light transmitted through the samples. We then have shown that this approach also works for mapping of a quantum state of light onto long-lived atomic spin state paving the road towards realization of the quantum memory for light. Recently we have also extended the free space light-atoms interface beyond the continuous variables in the proposal, where a coherent superposition "cat" state of an atomic ensemble is generated by a measurement sequence. Progress with other communication protocols such as atomic state teleportation and multiparty networks will be presented.
Quantum interfaces between polarized atomic ensembles and coherent states of light, applied recently to manipulate bipartite and multipartite entanglement, are revisited by means of a continuous-variable formalism. The explicit use of the continuous-variable formalism facilitates significantly the analysis of entanglement between different modes, reducing it to the study of the properties of a final covariance matrix which can be found analytically. Furthermore, it allows to study matter-light interfaces for mixed states, adapting the formalism to the experimental situations in which the initial prepared Gaussian states are, unavoidably, affected by a certain amount of noise. A multipartite scenario, leading to the generation of macroscopic cluster states is presented and analyzed in detail within this formalism.
Quantum networks are composed of quantum nodes which coherently interact by way of quantum channels. They offer powerful capabilities for quantum computation, communication, and metrology. A generic requirement for these realizations is the capability to generate and store quantum states among multiple quantum nodes, and to disseminate these resources throughout the network via the quantum channels. In this thesis, I describe a series of experiments whereby single excitations in atomic ensembles are strongly coupled to optical modes and provide efficient means for the coherent control of entangled states between matter and light. By following the seminal proposal by Duan et al., we have generated measurement-induced entanglement of an excitation between two cold atomic ensembles. Using this system, we investigated the relationship for the global bipartite entanglement and local correlations in its subsystems. In addition, we achieved functional quantum nodes for entanglement distribution. Two pairs of remote ensembles at two quantum nodes were prepared into entangled states in a heralded and asynchronous fashion by the conditional controls of the entanglement. The quantum states of the ensembles were then distributed into polarization entangled states of photons. We also prepared an analogous quantum state and transferred the nonlocal coherence between two pairs of heralded entangled atomic ensembles, providing a step towards entanglement connection. Beyond such probabilistic approaches, we demonstrated an experiment where entanglement between two quantum memories is created by the reversible and deterministic mapping of an entangled state of light via dynamic electromagnetically induced transparency. This experiment opens novel prospects of integrating hybrid quantum systems by way of reversible quantum interfaces between light and matter. Then, we extended our work to multipartite quantum systems. We theoretically investigated the characterization of multipartite mode-entangled states by way of quantum uncertainty relations, and introduced theoretical tools to verify the entanglement orders in multipartite systems. In particular, we achieved entanglement for one delocalized photon among multiple optical modes (N > 2). Finally, we have achieved measurement-induced entanglement of spin waves among four quantum memories. The individual atomic components for the entangled W state of the four ensembles were then coherently converted into four propagating entangled beams of light via superradiant emissions. We observed the statistical and dynamic transitions for the multipartite entangled spin waves. Experiments described in this thesis thereby represent significant advances of experimental and theoretical capabilities to generate, store, transfer, and characterize entanglement of matter and light over quantum networks.
Entanglement between two macroscopic atomic ensembles induced by measurement on an ancillary light system has proven to be a powerful method for engineering quantum memories and quantum state transfer. Here we investigate the feasibility of such methods for generation, manipulation, and detection of genuine multipartite entanglement (Greenberger-Horne-Zeilinger and clusterlike states) between mesoscopic atomic ensembles without the need of individual addressing of the samples. Our results extend in a nontrivial way the Einstein-Podolsky-Rosen entanglement between two macroscopic gas samples reported experimentally in [B. Julsgaard, A. Kozhekin, and E. Polzik, Nature (London) 413, 400 (2001)]. We find that under realistic conditions, a second orthogonal light pulse interacting with the atomic samples, can modify and even reverse the entangling action of the first one leaving the samples in a separable state.
In this thesis I explore the use of collective spin angular momentum as a platform for quantum information processing. Such systems have several nice features that make them excellent choices for such protocols, especially ones where information is also stored in photonic variables. The longer coherence times of atoms makes it possible to store information from light in atoms for future use, and it is generally easier to couple atomic variables than to create nonlinear interactions of light. Above and beyond the advantages of atomic systems, collective atomic systems have additional strengths. In the limit of a large number of atoms, the collective variables of atomic systems have a natural connection to the bosonic algebra of light (known as the Holstein-Primakoff or HP approximation) where components of the collective spin angular momentum effectively act as quadratures, making them natural systems for coupling to light. Also, collectively addressing the atoms allows one to access a large state space without individual addressing of the atoms. A natural first step towards control of these collective variables is generating large amounts of atomic spin squeezing. In the HP approximation going from rotations to squeezing corresponds to going from linear to quadratic interactions in the atomic quadratures; for extremely large squeezing one should see the breakdown of the HP approximation and the ability to generate arbitrary collective atomic states. I have sought to improve previous schemes for the spin squeezing of atomic ensembles, such as the proposal of Takeuchi et. al. based on coherent quantum feedback. In this scheme a beam of linearly polarized light passes through the atomic ensemble (prepared in a coherent state), coupling to the atoms through a state-dependent index of refraction (the Faraday effect). The light is then passed through a wave-plate and reflected back through the atoms for a second pass. This double-pass scheme leads to an effective nonlinearity as the atomic fluctuations are mapped onto the light on the first pass and then back on to the atoms in the second pass. The light acts as a bus coupling each atom to each of the others. This nonlinear interaction forms a shearing of the atomic coherent state that results in squeezing. The light is entangled to the atoms through these interactions, and remains entangled as it escapes the system. This leads to decoherence of the atoms as the light is lost to the environment, reducing the amount of spin squeezing achieved. The first step towards improving the double-pass scheme was to add a quantum eraser step in which the light is disentangled from the squeezed atoms. By first measuring one quadrature of the light, and then performing a measurement-dependent rotation on the atomic ensemble, it is possible to decouple the atoms and light so that the loss of the light does not reduce the atomic squeezing. This results in an improvement of the rate of atomic spin squeezing. The nonlinear shearing interaction that remains still falls short of the exponential squeezing seen in optical parametric amplification. The reason for this can be seen by decomposing the shearing interaction into squeezing along a given quadrature followed by a rotation. The rotation leads to a constantly changing axis along which the squeezing occurs, and thus the squeezing builds up more slowly. This can be corrected for by breaking up the light pulse into a sequence of small pulses, and performing a small phase matching rotation after each pulse. The squeezing then adds up along a constant direction, rather than along a constantly varying direction. This results in still further improvement of the rate of atomic spin squeezing. A complete model includes the effects of photon-atom scattering and other noise and loss effects on the overall rate of squeezing. Previous derivations of noise due to photon-atom scattering have started with the unjustified assumptions that the atomic and photonic decoherence channels were both Gaussian and independent of correlations between the two subsystems. They then proceed with very general statistical arguments that rely upon these simplifications. My work begins with the more fundamental master equation picture in which I find the Linblad jump operators. I find that in general the photonic and atomic loss channels are not independent, with the intensity of the light dictating the details of this dependence, and find the conditions under which the Gaussian approximation holds. Squeezing and loss is initially treated assuming ensembles of spin-1/2 atoms, but this work is further extended to higher dimensional subsystems. For a higher spin case, preparing the atoms in spin coherent states is not optimal. One can engineer a stronger interaction by preparing the atoms in an atomic "cat state", i.e., a superposition of the two stretch states along the direction of propagation of the light beam. The fluctuations of such a state are more strongly coupled to the light, resulting in a stronger nonlinearity. This leads to strong correlations between the atoms, but they are not immediately useful for squeezing; the cat state must be coherently mapped to a coherent state to achieve atomic spin squeezing. The state created in this manner is ultimately more squeezed than that achieved with the same interaction but prepared initially in a coherent state.