# NAME-QUAM

**INTRODUCTION**

The Project investigates ultra-cold atom/molecule quantum matter technology for quantum information computational tasks. Our efforts concentrate on atoms/molecules confined in periodic nanostructures, either externally imposed by optical lattices, or self-generated by atomic/molecular interactions. Parallel quantum processing in periodic nanostructures is expected to lead to significant advances in different areas of quantum information. The Project aims at developing novel techniques for quantum engineering and quantum control of ultra-cold atoms and molecules confined in the periodic nanostructures. An innovative aspect is the development of appropriate tools for achieving quantum control of strongly correlated many body systems at the nanoscale by exploiting moderate- and long-range quantum mechanical interactions. Strongly correlated interacting systems offer a level of computational power that cannot be reached with traditional qubits based on spin, or hyperfine atomic states. Moderate and long, range interactions will be exploited in few body quantum systems in order to produce fast quantum gates using novel robust qubit and/or qudit concepts and using quantum states with topological order, all of them highly relevant for next generation quantum information implementations.

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The objectives rely on the nano-design of atomic/molecular quantum matter at the mesoscopic scale of few-body systems. Generation and detection of multiparticle quantum entanglement, robustness of non-traditional qubits, quantum memories characterise our investigation. The Project will implement new quantum information technologies by achieving the following breakthroughs: characterizing long range interacting systems for optimal quantum information; realizing individual manipulation integrated in proper algorithms; designing new protected qubits or quantum information processors based on long range interactions; developing techniques for topological quantum computation; creating multi-partimulti-particle entanglement for quantum simulation investigations. At the present stage of the quantum information development our objectives are unique for the optical lattice quantum matter technology. As far as the visionary aspects are concerned, the technological and conceptual advances resulting from the planned investigations on multi-particle entanglement, topological structures and nano-optical engineering may lead to the identification of new directions and alternative approaches towards scalable and miniaturisable quantum information processing.

**PUBLISHABLE SUMMARY**

The NAMEQUAM Project investigates ultracold atom/molecule quantum matter technology for quantum information computational tasks. Parallel quantum processing in periodic nanostructures is expected to lead to significant advances in different areas of quantum information. The research efforts concentrate on atoms/molecules confined in periodic nanostructures, either externally imposed by optical lattices, or self-generated by atomic/molecular interactions. The Project aims at developing novel techniques for quantum engineering and quantum control of ultracold atoms and molecules confined in the periodic nanostructures. An innovative aspect is the development of appropriate tools for achieving quantum control of strongly correlated many body systems at the nanoscale by exploiting moderate- and long-range quantum mechanical interactions. Strongly correlated interacting systems offer a level of computational power that cannot be reached with traditional qubits based on spin, or hyperfine atomic states. Moderate and long, range interactions will be exploited in few body quantum systems in order to produce fast quantum gates using novel robust qubit, and/or qudit, concepts and using quantum states with topological order, all of them highly relevant for next generation quantum information implementations.

The objectives rely on the nanodesign of atomic/molecular quantum matter at the mesoscopic scale of few-body systems. Generation and detection of multiparticle quantum entanglement, robusteness of non-traditional qubits, quantum memories characterise the investigations. The Project will implement new quantum information technologies by achieving the following breakthroughs: characterizing long range interacting systems for optimal quantum information; realizing individual manipulation integrated in proper algorithms; designing new protected qubits or quantum information processors based on long range interactions; developing techniques for topological quantum computation; creating multi-particle entanglement for quantum simulation investigations.

At the present stage of the quantum information development NAMEQUAM objectives are unique for the optical lattice quantum matter technology. As far as the visionary aspects are concerned, the technological and conceptual advances resulting from the planned investigations on multi-particle entanglement, topological structures and nano-optical engineering may lead to the identification of new directions and alternative approaches towards scalable and miniaturisable quantum information processing. The final objectives of the project will provide a persistent and long-term commitment to emerging applications and will promote the transition towards a knowledge-based high-technology industry.

Few major breakthroughs of the overall Project are listed in the following.

The physical implementation of quantum information schemes based on optical lattices makes it necessary to address the open question of the individual addressability of single-site and single-qubit. Both I. Bloch group at JGUM-MPG and T. Esslinger group at ETHZ have obtained the first high-resolution images of ultracold atoms in an optical lattice where one clearly distinguishes individual atoms, as shown in the images of Fig. 1 from ref. [C. Weitenberg, M. Endres, J. F. Sherson, M. Cheneau, P. Schauß, T. Fukuhara, I. Bloch and S. Kuhr, *Single-Spin Addressing in an Atomic Mott Insulator*, Nature 471, 319-234 (2011)]. The observations of atomic densities down to the level of a single atom were used by ETHZ to measure local density fluctuations and density profiles of a Fermi gas in situ. In the quantum degenerate regime, the weakly interacting 6Li gas shows a suppression of the density fluctuations compared to the nondegenerate case, where atomic shot noise is observed [T. Müller, B. Zimmermann, J. Meineke, J.-P. Brantut, T. Esslinger, and H. Moritz, *Local Observation of Antibunching in a Trapped Fermi Gas*, Phys. Rev. Lett. 105, 040401 (2010)] . This manifestation of antibunching is a direct result of the Pauli principle and constitutes a local probe of quantum degeneracy. ETHZ analyzed the data using the predictions of the fluctuation-dissipation theorem and the local density approximation, demonstrating a fluctuation-based temperature measurement. Instead MPG has demonstrated how such control can be extended down to the most fundamental level of a single spin at a specific site of an optical lattice. Using a tightly focused laser beam together with a microwave field, MPG was able to flip the spin of individual atoms in a Mott insulator with sub-diffraction-limited resolution, well below the lattice spacing. MPG directly monitored the tunnelling quantum dynamics of single atoms in the lattice prepared along a single line and observed that our addressing scheme leaves the atoms in the motional ground state.

Fig. 1. Single-site addressing.

a, Experimentally obtained fluorescence image of a Mott insulator with unity filling in which the spin of selected atoms was flipped from |0> to |1> using the single-site addressing scheme. Atoms in state |1> were removed by a resonant laser pulse before detection. The lower part shows the reconstructed atom number distribution on the lattice. Each circle indicates a single atom, the points mark the lattice sites.bSame asa, but a global microwave sweep exchanged the population in |0> and |1>, such that only the addressed atoms were observed. The line inbshows 14 atoms on neighbouring sites.

ETHZ realized Quantum Optical Lattices by creating a Bose-Einstein condensate inside an ultrahigh-finesse cavity, so that a macroscopically populated mode of the matter wave field is strongly coupled to a single mode of the light field. Quantum optical lattices will provide robust qudits based on multi-particle interactions through the optical cavity mode. This configuration induces a completely new regime of interactions having an infinitely long range between the atoms, the condensate acting as a refractive index medium for the light field. In the experiment the condensate was trapped inside an ultrahigh-finesse optical cavity, and pumped from a direction transverse to the cavity axis. Two different momentum states play the role of the collective two-level system, and a spatial symmetry of the underlying lattice structure, given by the pump and cavity modes, is spontaneously broken. This steers the system into a self-organized phase with off-diagonal long-range order and a non-trivial diagonal long-range order. Thus the organized phase can be regarded as a supersolid similar to those proposed for two-component systems. ETHZ has been able to observe a quantum phase transition in this open system [K. Baumann, C. Guerlin, F. Brennecke and T. Esslinger, *Dicke quantum phase transition with a superfluid gas in an optical cavity*, Nature 464, 1301-1306 (2010)].

UIBK has developed a Rydberg quantum simulator. An universal quantum simulator is a controlled quantum device that reproduces the dynamics of any other many-particle quantum system with short-range interactions. In [H. Weimer, M. Müller, I. Lesanovsky, P. Zoller, and H.P. Büchler, *A Rydberg quantum simulator*, Nature Phys. 6, 382 (2010)] UIBK proposes that laser-excited Rydberg atoms in large-spacing optical or magnetic lattices provide an efficient implementation of a universal quantum simulator for spin models involving n-body interactions, including such of higher order. This would allow the simulation of Hamiltonians of exotic spin models involving n-particle constraints, such as the Kitaev toric code, colour code and lattice gauge theories with spin-liquid phases. In addition, this approach provides the ingredients for dissipative preparation of entangled states based on engineering n-particle reservoir couplings. The basic building blocks of this architecture are efficient and high-fidelity n-qubit entangling gates using auxiliary Rydberg atoms, including a possible dissipative time step through optical pumping, as in Fig. 2. This enables mimicking the time evolution of the system by a sequence of fast, parallel and high-fidelity n-particle coherent and dissipative Rydberg gates. A proof-of-principle of this idea has been recently tested experimentally using cold trapped ions, in a collaboration between theory and experiment in Innsbruck [.J.T. Barreiro, M. Müller, P. Schindler, D. Nigg, T. Monz, M. Chwalla, M. Hennrich, C.F. Roos, P. Zoller, R. Blatt, *An open-system quantum simulator with trapped ions*, Nature 470, 486-491 (2011)]

Figure 2:

a, Two internal states |A> and |B> give rise to an effective spin degree of freedom. These states are coupled to a Rydberg state |R> in two-photon resonance, establishing an electromagnetically induced transparency condition. On the other hand, the control atom has two internal states |0> and |1>. The state |1> can be coherently excited to a Rydberg state |r> and can be optically pumped into the state |0> for initializing the control qubit.b, For the toric code, the system atoms are located on the links of a two-dimensional square lattice, with the control qubits at the center of each plaquette for the interactions Ap and on the sites of the lattice for the interactions Bs.c,d, Set-up required for the implementation of the color code (c) and the U(1) lattice gauge theory (d).

Hexagonal structures play a particularly important role and lead to novel physics, such as that of carbon nanotubes or graphene. In [P. Soltan-Panahi, J. Struck, P. Hauke, A. Bick, W. Plenkers, G. Meineke, C. Becker, P. Windpassinger, M. Lewenstein and K. Sengstock,* Multi-component quantum gases in spin-dependent hexagonal lattices*, in press Nature Phys. (2011)] the realization of ultracold atoms in a spin-dependent optical lattice with hexagonal symmetry is reported by IFCO. IFCO has shown how the combined effects of the lattice and interactions between atoms lead to a forced antiferromagnetic Nöel order when two spin-components localize at different lattice sites. IFCO has also demonstrated that the coexistence of two components‚ (one Mott-insulating and the other one superfluid) leads to an interaction-induced modulation of the superfluid density, which is observed spectroscopically. The IFCO studies reveal the vast impact of the interaction-induced modulation on the superfluid-to-Mott-insulator transition.

UIBK has collaborated to experimentally realize the so-called sine-Gordon pinning quantum phase transition for strongly interacting bosons confined to a one-dimensional geometry. Typically, in quantum phases transitions the relative strength of two competing terms in the system’s Hamiltonian is changed across a finite critical value. However, For strongly-interacting quantum systems confined to lower-dimensional geometry a novel type of quantum phase transition may be induced for which an arbitrarily weak perturbation to the Hamiltonian is sufficient to drive the transition. This is shown in for a one-dimensional quantum gas of bosonic Cs atoms with tunable interactions, where UIBK has observed the commensurate-incommensurate quantum phase transition from a superfluid Luttinger liquid to a Mott-insulator [E. Haller, M. Gustavsson, M.J. Mark, J.G. Danzl, R. Hart, G. Pupillo, H.-C. Nägerl, *Observation of the commensurate/incommensurate quantum phase transition for a Luttinger Liquid of strongly interacting bosons*, Nature 466, 597–600 (2010)]. For sufficiently strong interactions, the transition is induced by adding an arbitrarily weak optical lattice commensurate with the atomic granularity, which leads to immediate pinning of the atoms. These results open up the experimental study of quantum phase transitions, and transport phenomena beyond Hubbard-type models in the context of ultracold gases.

Within the plan to prepare qubits based on Rydberg states CNR has produced excitation to high Rydberg states for a rubidium Bose-Einstein condensate. CNR has developed methods for detecting Rydberg excitations through the collection of charged ions/electrons with high efficiency. Making use of the dipole blockade associated to the Rydberg preparation, CNR has demonstrated the realization of one-dimensional chains of Rydberg excitations [M. Viteau, M.G. Bason, J. Radogostowicz, N. Malossi, D. Ciampini, O. Morsch, E. Arimondo, *Rydberg atoms in one-dimensional optical lattices*, arXiv:1103.4232] CNR has observed the excitation dynamics of up to 30 Rydberg states in a condensate occupying around 100 sites of a 1D optical lattice. The measurement of how many super-atoms fit into a self-assembled chain of a given size allowed a confirmation of the ‘super-atom’ picture of collective Rydberg excitations.

Long-range dipole-dipole interaction can have intriguing consequences for the properties of ultracold bosonic gases, such as as the formation of supersolids and the emergence metastable states in optical lattices). One particular consequence of that interaction is the coupling of spin and orbital angular momentum. A spin-polarized gas can reduce its spin-polarization while acquiring orbital rotation such that the total angular momentum is conserved. IFCO and IFAN [T. Świsłocki, T. Sowiński, J. Pietraszewicz, M. Brewczyk, K. Zakrzewski, M. Lewenstein, and M. Gajda, *Tunable dipolar resonances and the Einstein-de Haas effect in 87Rb atomic condensate*, arXiv:1102.1566] have suggested to realize this effect with ultracold 87Rb atoms in a cigar-shaped trap by applying a magnetic field, bridging the energy difference connected to the excitation of an orbital mode (chosen by a resonance condition for the magnetic field strength) of non-zero angular momentum. The IFCO-IFAN result is an important step towards exploring the role of additional atomic interactions on the quantum computing applications of OL's and realizing the generation of non-Abelian gauge fields for the three-component atomic motion.

The scattering properties of tightly trapped particles are deeply modified with respect to free space. Using a species-selective dipole potential (SSDP) to trap only K, leaving Rb essentially unaffected, LENS investigated experimentally the K-Rb scattering in confined geometry [G. Lamporesi, J. Catani, G. Barontini, Y. Nishida, M. Inguscio, and F. Minardi, *Scattering in Mixed Dimensions with Ultracold Gases*, Phys. Rev. Lett. 104, 153202 (2010)]. In this mixed-dimensional configuration an effective scattering length, depending on the free-space scattering length a and the confinement length l, describes the two-body scattering and displays resonant divergences for particular values of the *a/l* ratio. To experimentally detect such resonances, LENS recorded the atom losses by scanning the free-space scattering length in proximity of a Feshbach resonance. Indeed LENS observed a series of loss features whose position matched the predicted resonances of the effective scattering length. These mixed-dimensional resonances (MDR) occur because the center-of-mass and the relative motion are coupled. While for harmonically trapped identical particles such coupling is absent, this is not the case for heteronuclear mixtures in optical lattices, where the confinement can be largely different for the two species. No exploitable results, defined as knowledge having a potential for industrial or commercial application in research activities or for developing, creating or marketing a product or process or for creating or providing a service, are produced by this Project. The main target of the Project is to produce advanced and high quality basic knowledge to be exploited or used in further research.