Transport of Bose-Einstein condensates in magnetic microtraps, controllable by external parameters such as wire currents or radio-frequency fields, is studied within the framework of optimal control theory (OCT). We derive from the Gross-Pitaevskii equation the optimality system for the OCT fields that allow to efficiently channel the condensate between given initial and desired states. For a variety of magnetic confinement potentials we study transport and wavefunction splitting of the condensate, and demonstrate that OCT allows to drastically outperfrom more simple schemes for the time variation of the microtrap control parameters.

We derive scaling laws for the spin decoherence of neutral atoms trapped near conducting and superconducting plane surfaces. A result for thin films sheds light on the measurement of Y. J. Lin, I. Teper, C. Chin, and V. Vuletić ͓Phys. Rev. Lett. 92, 050404 ͑2004͔͒. Our calculation is based on a quantum-theoretical treatment of electromagnetic radiation near metallic bodies ͓P. K. Rekdal, S. Scheel, P. L. Knight, and E. A. Hinds, Phys. Rev. A 70, 013811 ͑2004͔͒. We show that there is a critical atom-surface distance that maximizes the spin relaxation rate and we show how this depends on the skin depth and thickness of the metal surface. In the light of this impedance-matching effect we discuss the spin relaxation to be expected above a thin superconducting niobium layer. Trapped neutral atoms have intrinsically long coherence times, making them suitable for many proposed applications based on quantum state manipulation. These include interferometry ͓1͔, low-dimensional quantum gas studies ͓2͔, and quantum information processing ͓3-5͔. The trapping structures required for these applications typically have feature sizes on the micron or submicron scale, sizes that are comparable with the atomic de Broglie wavelength. The required trap frequencies are typically in the 1 kHz to 1 MHz range, this being energetic enough to compete with the temperature and chemical potential and to allow adiabatic manipulation on the sub-ms time scale. One way to achieve these requirements is with intensity gradients of light, which make neutral atom traps by virtue of the optical dipole force. Major progress has been made with this approach ͓6-9͔, but still, the light is not arbitrarily configurable and it is difficult to address specific sites of an optical lattice. Structures microfabricated on a surface, known as atom chips, are emerging as a very promising alternative ͓10,11͔. These can be patterned in complex arrays on micrometer length scales. The locally addressed electric, magnetic, and optical fields on a chip provide great flexibility for manipulating and addressing the atoms. Magnetic traps on atom chips are commonly generated either by microfabricated current-carrying wires ͓11͔ or by poled ferromagnetic films ͓10,12͔ attached to some dielectric or metallic substrate. These are used to create local minima of the magnetic field strength in which low-fieldseeking alkali atoms are trapped by the Zeeman effect.In order to utilize atom chip structures of small scale, the atoms must be held close to the surface. However, this same proximity threatens to decohere the quantum state of the atoms through electromagnetic field fluctuations that occur in the vicinity of a surface. The free photon field does not perturb ground state alkali atoms appreciably, but the evanescent field modes associated with surface currents can be dense enough to generate significant rf noise. This effect arises because the resistivity of the surface material is always accompanied by field fluctuations as a consequence of the fluctuation-dissipation theore...

Using a consistent quantum-mechanical treatment for the electromagnetic radiation, we theoretically investigate the magnetic spin-flip scatterings of a neutral two-level atom trapped in the vicinity of a superconducting body. We derive a simple scaling law for the corresponding spin-flip lifetime for such an atom trapped near a superconducting thick slab. For temperatures below the superconducting transition temperature Tc, the lifetime is found to be enhanced by several orders of magnitude in comparison to the case of a normal conducting slab. At zero temperature the spin-flip lifetime is given by the unbounded free-space value.

In an exact quantum-mechanical framework we show that space-time expectation values of the second-quantized electromagnetic fields in the Coulomb gauge in the presence of a classical conserved source automatically lead to causal and properly retarded ÿ-independent electromagnetic field strengths. The classical ÿ-independent and gauge invariant Maxwell's equations naturally emerge in terms of quantum-mechanical expectation values and are therefore also consistent with the classical special theory of relativity. The fundamental difference between interference phenomena due to the linear nature of the classical Maxwell theory as considered in, e.g., classical optics, and interference effects of quantum states is clarified. In addition to these issues, the framework outlined also provides for a simple approach to invariance under time-reversal, some spontaneous photon emission and/or absorption processes as well as an approach to Vavilov-Čherenkov radiation. The inherent and necessary quantum uncertainty, limiting a precise space-time knowledge of expectation values of the quantum fields considered, is, finally, recalled.

In the present paper we study the spontaneous photon emission due to a magnetic spin-flip transition of a two-level atom in the vicinity of a dielectric body like a normal conducting metal or a superconductor. For temperatures below the transition temperature Tc of a superconductor, the corresponding spin-flip lifetime is boosted by several orders of magnitude as compared to the case of a normal conducting body. Numerical results of an exact formulation are also compared to a previously derived approximative analytical expression for the spin-flip lifetime and we find an excellent agreement. We present results on how the spin-flip lifetime depends on the temperature T of a superconducting body as well as its thickness H. Finally, we study how non-magnetic impurities as well as possible Eliashberg strong-coupling effects influence the spin-flip rate. It is found that non-magnetic impurities as well as strong-coupling effects have no dramatic impact on the spin-flip lifetime.It is well-known that the rate of spontaneous emission of atoms will be modified due to the presence of a dielectric body [1]. In current investigations of atom microtraps this issue is of fundamental importance since such decay processes have a direct bearing on the stability of e.g. atom chips.In magnetic microtrap experiments, cold atoms are trapped due to the presence of magnetic field gradients created e.g. by current carrying wires [2]. Such microscopic traps provide a powerful tool for the control and manipulation of cold neutral atoms over micrometer distances [3]. Unfortunately, this proximity of the cold atoms to a dielectric body introduces additional decay channels. Most importantly, Johnson-noise currents in the material give rise to electromagnetic field fluctuations. For dielectric bodies at room temperature made of normal conducting metals, these fluctuations may be strong enough to deplete the quantum state of the atom and, hence, expel the atom from the magnetic microtrap [4]. Reducing this disturbance from the surface is therefore strongly desired. In order to achieve this, the use of superconducting dielectric bodies instead of normal conducting metals has been proposed [5]. Some experimental work in this context has been done as well, e.g. by Nirrengarten et al. [6], where cold atoms were trapped near a superconducting surface.In the present article we will consider the spin-flip rate when the electrodynamic properties of the superconducting body are described in terms of either a simple two-fluid model or in terms of the detailed microscopic Mattis-Bardeen [7] and Abrikosov-Gor'kov-Khalatnikov [8] theory of weak-coupling BCS superconductors. In addition, we will also study how non-magnetic impurities, as well as strong coupling effects according to the lowfrequency limit of the Eliashberg theory [9], will affect the spontaneous emission rate.Following Ref.[10] we consider an atom in an initial state |i and trapped at position r A = (0, 0, z) in vacuum near a dielectric body. The rate Γ B of spontaneous and thermally stimul...