Johannes Otterbach

Photon-Photon Interactions via Rydberg Blockade

We develop the theory of light propagation under the conditions of electromagnetically induced transparency in systems involving strongly interacting Rydberg states. Taking into account the quantum nature and the spatial propagation of light, we analyze interactions involving few-photon pulses. We show that this system can be used for the generation of nonclassical states of light including trains of single photons with an avoided volume between them, for implementing photon-photon gates, as well as for studying many-body phenomena with strongly correlated photons.

Phonon-Induced Spin-Spin Interactions in Diamond Nanostructures: Application to Spin Squeezing

We propose and analyze a novel mechanism for long-range spin-spin interactions in diamond nanostructures. The interactions between electronic spins, associated with nitrogen-vacancy centers in diamond, are mediated by their coupling via strain to the vibrational mode of a diamond mechanical nanoresonator. This coupling results in phonon-mediated effective spin-spin interactions that can be used to generate squeezed states of a spin ensemble. We show that spin dephasing and relaxation can be largely suppressed, allowing for substantial spin squeezing under realistic experimental conditions. Our approach has implications for spin-ensemble magnetometry, as well as phonon-mediated quantum information processing with spin qubits.

Electromagnetically Induced Transparency with Rydberg Atoms

We present a theory of electromagnetically induced transparency in a cold ensemble of strongly interacting Rydberg atoms. Long-range interactions between the atoms constrain the medium to behave as a collection of superatoms, each comprising a blockade volume that can accommodate at most one Rydberg excitation. The propagation of a probe field is affected by its two-photon correlations within the blockade distance, which are strongly damped due to low saturation threshold of the superatoms. Our model is computationally very efficient and is in quantitative agreement with the results of the recent experiment of Pritchard et al. [Phys. Rev. Lett. 105, 193603 (2010)].

Dissipative preparation of spin squeezed atomic ensembles in a steady state.

We present and analyze a new approach for the generation of atomic spin-squeezed states. Our method involves the collective coupling of an atomic ensemble to a decaying mode of an open optical cavity. We demonstrate the existence of a collective atomic dark state, decoupled from the radiation field. By explicitly constructing this state we find that it can feature spin squeezing bounded only by the Heisenberg limit. We show that such dark states can be deterministically prepared via dissipative means, thus turning dissipation into a resource for entanglement. The scaling of the phase sensitivity taking realistic imperfections into account is discussed.

Wigner crystallization of single photons in cold Rydberg ensembles.

The coupling of weak light fields to Rydberg states of atoms under conditions of electromagnetically induced transparency leads to the formation of Rydberg polaritons which are quasiparticles with tunable effective mass and nonlocal interactions. Confined to one spatial dimension their low energy physics is that of a moving-frame Luttinger liquid which, due to the nonlocal character of the repulsive interaction, can form a Wigner crystal of individual photons. We calculate the Luttinger K parameter using density-matrix renormalization group simulations and find that under typical slow-light conditions kinetic energy contributions are too strong for crystal formation. However, adiabatically increasing the polariton mass by turning a light pulse into stationary spin excitations allows us to generate true crystalline order over a finite length. The dynamics of this process and asymptotic correlations are analyzed in terms of a time-dependent Luttinger theory.

Effective magnetic fields for stationary light.

We describe a method to create effective gauge potentials for stationary-light polaritons. When stationary light is created in the interaction with a rotating ensemble of coherently driven double-Lambda type atoms, the equation of motion is that of a massive Schrödinger particle in a magnetic field. Since the effective interaction area for the polaritons can be made large, degenerate Landau levels can be created with degeneracy well above 100. This opens up the possibility to study the bosonic analogue of the fractional quantum Hall effect for interacting stationary-light polaritons.

Confining stationary light: dirac dynamics and klein tunneling.

We discuss the properties of 1D stationary pulses of light in an atomic ensemble with electromagnetically induced transparency in the limit of tight spatial confinement. When the size of the wave packet becomes comparable or smaller than the absorption length of the medium, it must be described by a two-component vector which obeys the one-dimensional two-component Dirac equation with an effective mass m;{*} and effective speed of light c;{*}. Then a fundamental lower limit to the spatial width in an external potential arises from Klein tunneling and is given by the effective Compton length lambda_{C}=variant Plancks over 2pi/(m;{*}c;{*}). Since c;{*} and m;{*} can be externally controlled and can be made small, it is possible to observe effects of the relativistic dispersion for rather low energies or correspondingly on macroscopic length scales.

Bose-Einstein Condensation of Stationary-Light Polaritons

We propose and analyze a mechanism for Bose-Einstein condensation of stationary dark-state polaritons. Dark-state polaritons (DSPs) are formed in the interaction of light with laser-driven 3-level Lambda-type atoms and are the basis of phenomena such as electromagnetically induced transparency, ultraslow, and stored light. They have long intrinsic lifetimes and in a stationary setup, a 3D quadratic dispersion profile with variable effective mass. Since DSPs are bosons, they can undergo a Bose-Einstein condensation at a critical temperature which can be many orders of magnitude larger than that of atoms. We show that thermalization of polaritons can occur via elastic collisions mediated by a resonantly enhanced optical Kerr nonlinearity on a time scale short compared to the decay time. Finally, condensation can be observed by turning stationary into propagating polaritons and monitoring the emitted light.

Photonic Phase Gate via an Exchange of Fermionic Spin Waves in a Spin Chain

We propose a new protocol for implementing the two-qubit photonic phase gate. In our approach, the π phase is acquired by mapping two single photons into atomic excitations with fermionic character and exchanging their positions. The fermionic excitations are realized as spin waves in a spin chain, while photon storage techniques provide the interface between the photons and the spin waves. Possible imperfections and experimental systems suitable for implementing the gate are discussed.

From Anderson to anomalous localization in cold atomic gases with effective spin–orbit coupling

We study the dynamics of a spin–orbit (SO)-coupled Schrodinger particle with two internal degrees of freedom moving in a one-dimensional random potential. Numerical calculation of the density of states reveals the emergence of a Dyson-like singularity at zero energy when the system approaches the quasi-relativistic limit of the random-mass Dirac model for large SO coupling. Simulations of the expansion of an initially localized wave-packet show a crossover from an exponential (Anderson) localization to an anomalous power-law behavior reminiscent of the zero-energy (mid-gap) state of the random-mass Dirac model. We discuss conditions under which the crossover is observable in an experiment and derive the zero-energy state, thus proving its existence under proper conditions. Finally we describe a possible experimental realization using an ensemble of cold 87Rb-atoms interacting with external control lasers and speckle fields.