**Max-Planck-Institute of Quantum Optics (MPQ) **

http://www.mpq.mpg.de/cms/mpq/en/index.html

Principal Investigator: Prof. Ignacio Cirac

**Light-matter Interaction for Small Atomic Ensembles**

We theoretically analyze the light-matter interaction in the case of

small ensembles. We investigate the limits of miniaturization and what requirements are to be met to still achieve strong enough coupling.

We develop efficient interface protocols adapted to the microscopic

dimensions of the cell using stroboscopic interactions to engineer

effective Hamiltonians or employing adiabatic passage techniques.

For state preparation we will also study dissipative approaches and

their combination with feedback operations.

In particular, we explore the potential of the small ensembles to

generate non-Gaussian states and operations. These states and

operations represent an important resource for quantum information

processing purposes as they allow to circumvent the limitations of the

more easily implemented purely Gaussian setting. For large ensembles the atom-light interaction is very well described by the Holstein-Primakoff approximation (HPA) which leads to a bilinear coupling between light and collective atomic variables. We investigate if for small ensembles higher order corrections to the HPA might allow to go beyond the quadratic (Gaussian) setting.

More generally, we are developing a theoretical framework to describe the mapping between collective excitations and photons including dipole-dipole interactions and multiple light scattering under different trapping conditions in order to understand how to use the control on the states of the trapped atoms to generate interesting

quantum states of light.

Figure 1: Two atomic ensembles interacting with a laser beam. Light-matter interaction involving a strong y-polarized laser field (depicted in green) and two atomic ensembles, which are spin polarized parallel and antiparallel with respect to a homogeneous magnetic field oriented along x. Atoms are as- sumed to posses two ground and two excited states |↑ , |↓ and |e↑ , |e↓ ,

The strong resonant driving field induces diagonal transitions |↑ → |e↓ and |↓ → |e↑ and which lead to the emission of photons with x-polarization (corresponding to the transitions |↑ → |e↑ and |↓ → |e↓ ). Due to the Zeeman splitting Ω of the atomic ground states, photons are scattered into the upper and lower sideband (shown in blue and red respectively) of the incident field.

**Probing dynamical quantum correlations**

We have proposed a method to optically measure dynamical quantum correlations in strongly correlated atomic systems. The scheme combines quantum nondemolition detection of atomic observables with quantum memories. The former probes the quantity of interest, mapping it to the light field, which is, in turn, stored in the quantum memory until at a later time a second beam probes again the strongly correlated atoms and reads out the stored information from the memory.

Figure 2: (a,b) Schematic representation as a quantum circuit of the proto- col to measure dynamical correlations. S (M) is the many body system (the quantum memory), and Li is the i-th light beam used in the protocol. (a) Scheme for measuring at two different instances of times, which after repetition give FS (t). (b) Scheme to measure FM (t) by using a quantum memory.

(c) Signal obtained in probing the quantum many-body dynamics of coupled double-well superlattices. The results are obtained with exact diagonalization for a chain of 12 spins. Filled red circles and dashed line show the Fourier transform of the symmetrized two-time dynamical correlation function FM (t), the empty blue squares and solid line correspond to the Fourier transform of FS (t). Vertical dashed green lines show the spectrum of the Hamiltonian.

**MPG Group **

Prof. Dr. J. Ignacio Cirac (group leader)

Dr. Geza Giedke (postdoc)

Dr. Oriol Romero-Isart (postdoc)

Dr. Christine Muschik (researcher)

Dr. Carlos Navarrete-Benlloch (postdoc)

**Publications**

Muschik, C. A.; Krauter, H.; Hammerer, K. & Polzik, E. S. Quantum Information at the Interface of Light with Mesoscopic Objects (2011)arXiv:1105.2947 – http://arxiv.org/abs/1105.2947

Romero-Isart, O.; Rizzi, M.; Muschik, C. A.; Polzik, E. S.; Lewenstein, M. & Sanpera, A. Quantum Memory Assisted Probing of Dynamical Spin Correlations (2011) – arXiv:1105.6308 http://arxiv.org/abs/1105.6308