# Project Area A:

Tuning quantum correlations

It is one of our main goals to generate new states of matter by controlling quantum correlations. Tailored quantum matter can often be represented in terms of real or pseudo spin systems. On the one hand, these systems are very versatile and may describe rather complex physical situations. On the other hand, they are often simple enough to be controlled experimentally and captured mathematically. Moreover, they offer vast possibilities to tune the inherent quantum correlations by adjusting the relevant parameters. Often, not only the system’s geometry and dimension can be modified, but also the various coupling mechanisms within the system and with the environment can be controlled. Quantum correlations in the ground state of these interacting quantum manybody systems may be rather complex and provide a rich phenomenology. In project area A, we focus our efforts on the possibility to tune quantum correlations in a variety of spin, pseudo spin and many-body systems. Major goals of the projects grouped in area A are (i) to find new states of matter and (ii) to develop localized quantum optical probes to measure decoherence processes in solids and coupled solid state systems.

Project A1 is devoted to the investigation and control of coherence and correlation effects in semiconductor quantum dot systems. Quantum correlations determine the electron transport through the quantum dot. Tunable parameters are (i) the strength of the tunneling coupling between the quantum dot spin and the environment (e.g. leads) by gate voltages, (ii) the splitting of the spin states by externally applied magnetic fields, and (iii) the number of electrons on the quantum dot. The main goal of the second funding period is to investigate in general the interaction between two well-characterized quantum dots which are in close vicinity and share common leads. An arrangement of two quantum dots should give rise to a tunable system of two Kondo impurities (i.e. quantum dots with spindegeneracy) coupled by a common lead of variable path length between the dots, which allows one to experimentally investigate the existence of a Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction. The project is directly related to the project A6, where similar arrangements of coupled quantum dots will be investigated theoretically and the nature of the RKKY interaction between the dots is characterized. The interaction between quantum dots will also be investigated in project C3, where the optical coupling between quantum dots is addressed. Furthermore, common technological interests and similarities with regard to state of the art measurement techniques provide the background for a strong collaboration between this project and C9 in which high-quality nanostructures are fabricated.

Project A2 is focused on the experimental study of dipolar Bose-Einstein condensates. In a dipolar Bose-Einstein condensate, the dominant inter-atomic interaction is the dipoledipole interaction. Since this interaction is anisotropic and long-range, it leads to interesting new physical behavior compared to an ordinary Bose-Einstein condensate with isotropic van der Waals interaction. The project will extend the studies on the stability and collapse of dipolar gases to low-dimensional Bose-Einstein condensates and to Bose-Fermi mixtures of two isotopes of chromium. Here a roton-type instability in the Bose gas is predicted, which results in a fragmentation of the condensate via density waves. The aim is the creation of a novel state of matter with well controlled quantum correlations between the atoms. A second focus is on the investigation of S=3 spinor condensates of chromium atoms as well as experiments in mesoscopic multiple-well potentials. The dipole-dipole interaction is expected to lead to a rich landscape of different localized and superfluid states depending on the energy scales of on-site interactions, next neighbor interaction, and tunneling. The strongly correlated many-body aspects provide a strong link of this project to the project area B: the project will be performed in close cooperation with the theoretical project B8 working on dipolar systems. The project B7 aiming at the production of heteronuclear molecules from a two component gas is also naturally linked, and experience in sympathetic cooling techniques will be exchanged. The project B6 on Rydberg gases deals – although in a frozen situation – with long range interactions.

Project A3 bridges the gap between atomic and solid state physics by coupling the electronic spin of molecular nanomagnets to a strong photon field. The magnetic moment of the molecules is used as a quantum degree of freedom coupled to a planar microwave resonator. A careful engineering of the resonator design and the ensemble of magnetic molecules, we will reach the strong coupling limit and enter the field of cavity quantum electrodynamics (QED) with controlled matter-light states. In contrast to the established approaches to cavity- and circuit-QED, in this project the magnetic component of the light field is coupled to the molecules. This way, the universal properties of (molecular) spin systems are combined with the convenient access of solid-state systems. Magnetic molecules can form crystals or can be embedded in a solid-state matrix while maintaining their fundamentally molecular properties: the macroscopic magnetic response of such a solid sample can be described as a quantum mechanical ensemble of identical molecules. The long-term objective is the creation of hybrid quantum systems and the exploration of quantum control by utilizing nanomagnets. The project adopts the concepts of strong coupling and cavity QED, and thus greatly profits from the experience and knowledge that is available in the SFB from groups working on cold atoms and ions. The aspect of studying the cooperative effects of the many-body system opens a strong link to project B6, where Rydberg atoms constitute a comparable spin system: a mesoscopic ensemble of spins is studied and similar questions (“What are the signatures of collective behavior in our system?”) are addressed. When it comes to the single quantum system, i.e. molecular spins in a solid, fundamental questions are addressed that are also at the core of other projects within the SFB: decoherence of spin systems in a solid are also studied in projects C3 and C4, where single (or a few individual) spins are isolated and controlled in optical quantum dots and defect centers in diamond, respectively.

Project A5 concentrates on fractional Josephson vortices in the quantum regime. Semifluxons, which are Josephson vortices that carry only one half of the magnetic flux quantum, behave as spin-1/2 systems, since they act as small magnets with two possible orientations. Two or more semifluxons interact via overlapping supercurrents as well as via magnetic dipole-dipole interaction. While in the first funding period, the focus was on single fractional vortices, the second period will be dedicated to many interacting fractional vortices: ranging from two-vortex molecules up to 1D fractional vortex "crystals". Within this tailored matter state, the interactions between the vortices in a "crystal" can be tuned electronically by changing their topological charge, bias current or magnetic field, providing a good control over their quantum properties. From the theoretical side, the collective coordinate approach will be extended from semifluxons to arbitrary fractional vortices. In addition, the investigations done so far opened new avenues to create tailored and tunable vortex matter in the quantum regime. Examples in project A5 are fully tunable double well potentials, as well as annular Josephson junctions containing both mobile integer fluxons and pinned fractional vortices. Such systems may be considered as artificial molecules with tunable interactions. The quantum "chemistry" of these vortex molecules may share many analogies to their cold molecule counterparts. The project has a link to project A2, where the Josephson effect in Bose-Einstein condensates plays an important role. A connection with the project C2 is established, as C2 uses superconducting structures with embedded fractional vortices to study interactions between tunable Josephson systems and cold atoms. Furthermore, the numerical simulation tools for π-junctions will be further developed together with C8, where superconducting Josephson junctions, SQUIDs and resonators are investigated, and the dynamics of vortices is explored;-->Also project A3 will profit from these developments.

The aim of project A6 is the study of electrical transport through quantum dots beyond linear response theory, i.e. with a finite bias, in situations where strong correlations dominate. The numerical studies should be carried out by means of the time-dependent density matrix renormalization group (DMRG) method. The results are expected to be instrumental for the quantum control of complex quantum dot systems. The focus is on systems with quantum dots interacting via common electronic reservoirs. In the case of two quantum dots in the Kondo regime coupled by a common lead, the competition between the Kondo scale and the Ruderman-Kittel-Kasuya-Yoshida (RKKY) interaction is analyzed. This problem is of interest not only in the field of mesoscopic systems but also for heavy fermion compounds, and hence, it is of general interest in condensed matter physics. Going from single quantum dots to several interacting dots, new aspects on the dynamics of such complex systems are expected. These may help to understand the transition from few- to many-body states in coupled quantum dots. The project is closely connected to the project A1, where quantum dots in the Kondo regime are being studied, and the configurations for the theoretical study will be adapted to the ones studied experimentally in A1. In addition, the project shares the aspect of non-equilibrium and coherent time evolution studied theoretically and experimentally in B6 via the dynamics of Rydberg states coherently excited from an ultra cold atomic gas.

The main focus of project A7 is to investigate the interaction between ultracold ions and neutral atoms in traps. The available control of the geometry, strength of trapping potentials and of external fields will be exploited in order to generate a time dependent tuning of quantum correlations in combined systems of ions and atoms. Starting with well controlled few-body systems that can still be theoretically treated, the scaling towards the many-body quantum system will be analyzed. The aim of the analysis of ion-atom interactions over a broad range of distances is to achieve control over their quantum states and to engineer and investigate interesting quantum correlations in experimentally realizable systems. Analogies to collective effects in condensed-matter systems will be explored, for instance concerning effective ion-mediated interactions between atoms. A further important application of this work will be the analysis of the interactions between ions and neutral molecules, which will establish an important link to project B6, where such interactions are expected to play a role. On the one hand, this project has direct links with the experimental study of microscopic atom and ion traps (projects C2 and C5 respectively). They represent naturally preferred candidates for the realization of the interaction schemes that will be developed and analyzed here. Novel trapping concepts as those proposed in project C9 are also relevant in this context. Moreover, the idea of a (charged) defect interacting with an ensemble of neutral particles bears a definite analogy with the solid-state systems investigated in project C4 – in a way, colour centres in diamond can be regarded as a kind of “solid-state ion trap”, and also in that context a lot of the interesting physics deals with the quantum interactions between the defect and the surrounding atoms. Exchange and collaboration with other theory groups from Section B, “Controlling quantum phase transitions”, will be beneficial especially for the part concerning the engineering of many-body coupled atom-ion systems, in both directions: supplying interesting problems to their numerical expertise, and feeding back the results into the analysis of relevant atom-ion processes. The use of time-dependent density matrix renormalization group techniques (t-DMRG), as employed in projects A6 and B4, appears as a most suited collaboration vector in this sense.