Martin Kiffner

Two-mode single-atom laser as a source of entangled light

A two-mode single-atom laser is considered, with the aim of generating entanglement in macroscopic light. Two transitions in the four-level gain medium atom independently interact with the two cavity modes, while two other transitions are driven by control laser fields. Atomic relaxation as well as cavity losses are taken into account. We show that this system is a source of macroscopic entangled light over a wide range of control parameters and initial states of the cavity field.

Vacuum-Induced Processes in Multilevel Atoms

Publisher Summary Atoms commonly do not act as isolated objects, but rather are open quantum systems, as they interact with the environment. Typically, this environment is formed by the electromagnetic vacuum field. The interaction of atoms with the environment modifies the atomic dynamics, with spontaneous emission as the most obvious example. Spontaneous emission is generally recognized as incoherent process, which leads to decoherence and, therefore, forms a major limitation for many schemes of current theoretical and experimental interest. But vacuum-induced processes can also generate coherent time evolution. These coherences can be interpreted as arising from vacuum-induced transitions between different atomic states. The situation becomes even more interesting if different atoms can exchange energy via the vacuum. Such dipole–dipole interactions induce both coherent and incoherent atomic dynamics, leading to significant deviations from the single-atom properties. Finally, a complex interplay of vacuum-induced interatomic and intraatomic dynamics may arise if several multilevel atoms are considered. These vacuum-induced processes form the basis for a large number of applications, for which the vacuum-induced dynamics can be favorable, perturbing, or even both. Most applications can be improved, if the vacuum-induced processes can be modified or even controlled. Thus, a profound understanding of vacuum-induced processes is desirable. Motivated by this, this chapter discusses vacuum-induced processes in multilevel atoms.

Dissipation-induced Tonks-Girardeau gas of polaritons

A scheme for the generation of a Tonks-Girardeau (TG) gas of polaritons with purely dissipative interaction is described. We put forward a master equation approach for the description of stationary light in atomic four-level media and show that, under suitable conditions, two-particle decays are the dominant photon loss mechanism. These dissipative two-photon losses increase the interaction strength by at least one order of magnitude as compared to dispersive two-photon processes and can drive the polaritons into the TG regime. Characteristic correlations of the TG gas, including quantities that distinguish it from free fermions, can be measured via standard quantum optical techniques. Our scheme thus allows one to feasibly generate highly correlated photon states, which can be of considerable use in quantum-information processing and precision measurements.

Three-body bound states in dipole-dipole interacting Rydberg atoms.

We show that the dipole-dipole interaction between three identical Rydberg atoms can give rise to bound trimer states. The microscopic origin of these states is fundamentally different from Efimov physics. Two stable trimer configurations exist where the atoms form the vertices of an equilateral triangle in a plane perpendicular to a static electric field. The triangle edge length typically exceeds R≈2 μm, and each configuration is twofold degenerate due to Kramers degeneracy. The depth of the potential wells and the triangle edge length can be controlled by external parameters. We establish the Borromean nature of the trimer states, analyze the quantum dynamics in the potential wells, and describe methods for their production and detection.

Magnetic monopoles and synthetic spin-orbit coupling in Rydberg macrodimers.

We show that sizable Abelian and non-Abelian gauge fields arise in the relative motion of two dipole-dipole interacting Rydberg atoms. Our system exhibits two magnetic monopoles for adiabatic motion in one internal two-atom state. These monopoles occur at a characteristic distance between the atoms that is of the order of one micron. The deflection of the relative motion due to the Lorentz force gives rise to a clear signature of the effective magnetic field. In addition, we consider nonadiabatic transitions between two near-degenerate internal states and show that the associated gauge fields are non-Abelian. We present quantum mechanical calculations of this synthetic spin-orbit coupling and show that it realizes a velocity-dependent beam splitter.

Coherent control in a decoherence-free subspace of a collective multilevel system

Decoherence-free subspaces (DFSs) in systems of dipole-dipole interacting multilevel atoms are investigated theoretically. It is shown that the collective state space of two dipole-dipole interacting four-level atoms contains a four-dimensional DFS. We describe a method that allows us to populate the antisymmetric states of the DFS by means of a laser field, without the need for a field gradient between the two atoms. We identify these antisymmetric states as long-lived entangled states. Further, we show that any single-qubit operation between two states of the DFS can be induced by means of a microwave field. Typical operation times of these qubit rotations can be significantly shorter than for a nuclear spin system.

Dipole-dipole-coupled double-Rydberg molecules

We show that the dipole-dipole interaction between two Rydberg atoms can give rise to long range molecules. The binding potential arises from two states that converge to different separated atom asymptotes. These states interact weakly at large distances, but start to repel each other strongly as the van der Waals interaction turns into a resonant dipole-dipole interaction with decreasing separation between the atoms. This mechanism leads to the formation of an attractive well for one of the potentials. If the two separated atom asymptotes come from the small Stark splitting of an atomic Rydberg level, which lifts the Zeeman degeneracy, the depth of the well and the location of its minimum are controlled by the external electric field. We discuss two different geometries that result in a localized and a donut shaped potential, respectively.

Breakdown of the few-level approximation in collective systems

The validity of the few-level approximation in dipole-dipole interacting collective systems is discussed. As an example system, we study the archetype case of two dipole-dipole interacting atoms, each modeled by two complete sets of angular momentum multiplets. We establish the breakdown of the few-level approximation by first proving the intuitive result that the dipole-dipole induced energy shifts between collective two-atom states depend on the length of the vector connecting the atoms, but not on its orientation, if complete and degenerate multiplets are considered. A careful analysis of our findings reveals that the simplification of the atomic level scheme by artificially omitting Zeeman sublevels in a few-level approximation generally leads to incorrect predictions. We find that this breakdown can be traced back to the dipole-dipole coupling of transitions with orthogonal dipole moments. Our interpretation enables us to identify special geometries in which partial few-level approximations to two- or three-level systems are valid.

Probing quantum superposition states with few-cycle laser pulses

The quantum dynamics of a two-level system illuminated by a few-cycle pulse with an adjustable carrier-envelope (C-E) phase is investigated theoretically. We consider the weak-field regime where tunneling processes and multiphoton ionization are negligible. It is shown that the upper state population exhibits a strong dependence on the C-E phase and on the time of arrival of the few-cycle pulse if the system is initially prepared in a coherent superposition state. We demonstrate that this effect can be employed to probe the coherence properties of the superposition state and allows one to determine the phase of the laser that prepares this state.

Two-way interconversion of millimeter-wave and optical fields in Rydberg gases

We show that cold Rydberg gases enable an efficient six-wave mixing process where terahertz or microwave fields are coherently converted into optical fields and vice versa. This process is made possible by the long lifetime of Rydberg states, the strong coupling of millimeter waves to Rydberg transitions and by a quantum interference effect related to electromagnetically induced transparency (EIT). Our frequency conversion scheme applies to a broad spectrum of millimeter waves due to the abundance of transitions within the Rydberg manifold, and we discuss two possible implementations based on focussed terahertz beams and millimeter wave fields confined by a waveguide, respectively. We analyse a realistic example for the interconversion of terahertz and optical fields in rubidium atoms and find that the conversion efficiency can in principle exceed 90\%.