Quantum optics: Dedication

Elementary Theory of Angular Momentum. By M. E. Rose. Pp. x, 248. 80s. 1957. (Wiley)

Entanglement-based technologies, such as quantum information processing, quantum simulations and quantum-enhanced metrology, have the potential to revolutionize our way of computing and measuring, and help clarify the puzzling concept of entanglement itself. Ultracold atoms on atom chips are attractive for their implementation, as they provide control over quantum systems in compact, robust and scalable set-ups. An important tool in this system is a potential depending on the internal atomic state. Coherent dynamics in such a potential combined with collisional interactions enables entanglement generation both for individual atoms and ensembles. Here, we demonstrate coherent manipulation of Bose-condensed atoms in a state-dependent potential, generated with microwave near-fields on an atom chip. We reversibly entangle atomic internal and motional states, realizing a trapped-atom interferometer with internal-state labelling. Our system provides control over collisions in mesoscopic condensates, paving the way to on-chip generation of many-particle entanglement and quantum-enhanced metrology with spin-squeezed states. Simultaneous coherent control of internal and motional states of a Bose–Einstein condensate has been demonstrated on an ‘atom chip’. The method should provide a route to generating many-particle entangled states, which are needed for entanglement-based technologies such as quantum-information processing or quantum-enhanced metrology.

Coherent manipulation of Bose–Einstein condensates with state-dependent microwave potentials on an atom chip

Atom interferometers provide record precision in measurements of a broad range of physical quantities. Extending atom interferometry to micrometer spatial resolution would enable new applications in electromagnetic field sensing, surface science, and the search for fundamental short-range interactions. I present experiments where we use a small Bose-Einstein condensate on an atom chip as an interferometric scanning probe to map out a microwave field at distances down to $16$ micrometer from the chip surface with a few micrometers spatial resolution. By creating entanglement between the atoms, our interferometer overcomes the standard quantum limit of interferometry by 4 dB in variance and maintains enhanced performance for interrogation times up to 10 ms. This corresponds to a microwave magnetic field sensitivity of 77 pT/sqrt(Hz) in a probe volume of 20 cubic micrometer. High-resolution measurements of microwave near-fields, as demonstrated here, are important for the development of integrated microwave circuits for quantum information processing and applications in communication technology.

Quantum metrology with entangled atoms is particularly useful in measurements with high spatial resolution, since the atom number in the probe volume is limited by collisional losses. I analyze the effect of such density-dependent losses in high-resolution atom interferometry, and show that there is a strict upper limit on the useful number of atoms. Our experimental results indicate that even tighter limits on the particle number and interrogation time may arise from density-dependent dephasing, and provide a starting point for future studies towards the fundamental limits of coherence in Bose-Einstein condensates. Our experimental setup is ideally suited to experimentally address these questions, and provides a promising platform for further studies on quantum metrology and entanglement in many-particle atomic systems.

Quantum metrology with a scanning probe atom interferometer

Demonstration of quantum entanglement, a key resource in quantum computation arising from a nonclassical correlation of states, requires complete measurement of all states in varying bases. By using simultaneous measurement and state tomography, we demonstrated entanglement between two solid-state qubits. Single qubit operations and capacitive coupling between two super-conducting phase qubits were used to generate a Bell-type state. Full two-qubit tomography yielded a density matrix showing an entangled state with fidelity up to 87%. Our results demonstrate a high degree of unitary control of the system, indicating that larger implementations are within reach.

http://absimage.aps.org/image/MAR07/MWS_MAR07-2006-005340.pdf

Direct Measurement of the Entanglement of Two Superconducting Qubits via State Tomography.

In this thesis, I report experiments and theoretical work on the coherent manipulation of ultracold atoms on an atom chip. We experimentally investigate the effect of the atom chip surface on internal-state coherence and demonstrate a chip-based atomic clock. Theoretical proposals are made for a robust atom chip quantum gate and for the coupling of a Bose-Einstein condensate to a nanoelectromechanical system. In our experiments, we trap atoms in a magnetic microchip trap and prepare them in a coherent superposition of two internal states with nearly identical magnetic moments. By performing Ramsey interferometry we investigate the effect of atom-surface interactions on internal-state coherence. Trap and coherence lifetimes exceeding 1 s are observed with atoms at distances of 5 − 130 μm from the chip surface. The coherence lifetime in the chip trap agrees well with the results of similar measurements in macroscopic magnetic traps. At distances below 5 μm, loss of atoms occurs due to the attractive Casimir-Polder surface potential. We make use of the good coherence properties to demonstrate a chipbased atomic clock and measure its relative frequency stability to 1.7 × 10−11 (τ [s])−1/2. Our measurements show that with straightforward improvements a relative stability in the 10−13 (τ [s])−1/2 range is realistic. An atom chip clock may find applications as a portable secondary standard and in satellite navigation. We propose to use our state pair for quantum information processing and describe a realistic implementation of a collisional quantum phase gate on an atom chip. In our proposal, a key role is played by state-selective microwave near-field potentials. These potentials are a useful new tool for atom chip experiments. They combine the versatility of optical dipole traps with the dissipationless character of static magnetic potentials and the adjustable geometry of a near-field trap. We describe the design and fabrication of a multi-layer atom chip for experiments with microwave near-fields. The work reported here shows that atom chips are a versatile system for quantum engineering. Moreover, atom chips enable new and intriguing experiments at the boundary between quantum optics and condensed matter physics. As an example, we propose to couple a Bose-Einstein condensate to the mechanical oscillations of a nanoscale cantilever with a magnetic tip. This system realizes a mechanical analog of cavity quantum electrodynamics, with the possibility to reach the strong coupling regime.

Garching Max-Planck-Institut für Quantenoptik

Papers

Coherent manipulation of ultracold atoms an atom chips