[Show abstract][Hide abstract] ABSTRACT: Even though quantum systems in energy eigenstates do not evolve in time, they can exhibit correlations between internal degrees of freedom in such a way that one of the internal degrees of freedom behaves like a clock variable, and thereby defines an internal time, that parametrizes the evolution of the other degrees of freedom. This situation is of great interest in quantum cosmology where the invariance under reparametrization of time implies that the temporal coordinate dissapears and is replaced by the Wheeler-DeWitt constraint. Here we show that the emergent character of an internal time variable can be investigated experimentally using the exquisite control now available on moderate-size quantum systems. We describe in detail how to implement such an experimental demonstration using the spin and motional degrees of freedom of a single trapped ion.
Full-text · Article · Sep 2015 · Physical Review A
[Show abstract][Hide abstract] ABSTRACT: Even though quantum systems in energy eigenstates do not evolve in time, they
can exhibit correlations between internal degrees of freedom in such a way that
one of the internal degrees of freedom behaves like a clock variable, and
thereby defines an internal time, that parametrises the evolution of the other
degrees of freedom. This situation is of great interest in quantum cosmology
where the invariance under reparametrisation of time implies that the temporal
coordinate dissapears and is replaced by the Wheeler-DeWitt constraint. Here we
show that this paradox can be investigated experimentally using the exquisite
control now available on moderate size quantum systems. We describe in detail
how to implement such an experimental demonstration using the spin and motional
degrees of freedom of a single trapped ion.
[Show abstract][Hide abstract] ABSTRACT: The addressing of a particular qubit within a quantum register is a key pre-requisite for scalable quantum computing. In general, executing a quantum gate with a single qubit, or a subset of qubits, affects the quantum states of all other qubits. This reduced fidelity of the whole-quantum register could prevent the application of quantum error correction protocols and thus preclude scalability. Here we demonstrate addressing of individual qubits within a quantum byte (eight qubits) and measure the error induced in all non-addressed qubits (cross-talk) associated with the application of single-qubit gates. The quantum byte is implemented using microwave-driven hyperfine qubits of (171)Yb(+) ions confined in a Paul trap augmented with a magnetic gradient field. The measured cross-talk is on the order of 10(-5) and therefore below the threshold commonly agreed sufficient to efficiently realize fault-tolerant quantum computing. Hence, our results demonstrate how this threshold can be overcome with respect to cross-talk.
Full-text · Article · Aug 2014 · Nature Communications
[Show abstract][Hide abstract] ABSTRACT: Dephasing -- phase randomization of a quantum superposition state -- is a
major obstacle for the realization of high fidelity quantum logic operations.
Here, we implement a two-qubit Controlled-NOT gate using dynamical decoupling
(DD), despite the gate time being more than one order of magnitude longer than
the intrinsic coherence time of the system. For realizing this universal
conditional quantum gate, we have devised a concatenated DD sequence that
ensures robustness against imperfections of DD pulses that otherwise may
destroy quantum information or interfere with gate dynamics. We compare its
performance with three other types of DD sequences. These experiments are
carried out using a well-controlled prototype quantum system -- trapped atomic
ions coupled by an effective spin-spin interaction. The scheme for protecting
conditional quantum gates demonstrated here is applicable to other physical
systems, such as nitrogen vacancy centers, solid state nuclear magnetic
resonance, and circuit quantum electrodynamics.
Full-text · Article · May 2013 · Physical Review Letters
[Show abstract][Hide abstract] ABSTRACT: We report on microwave sideband cooling of trapped 171Yb+ ions. Different to laser cooling, microwave sideband cooling requires an additional mechanism that allows to couple internal states of a trapped ion with its vibrational states. This is done in the presence of a static magnetic field gradient created by two permanent magnets. Cooling is achieved by repetitions of the following two steps: First, microwave radiation, tuned to the red sideband of the hyperfine transition F=0 ↔ F=1 in the electronic ground state S1/2 of 171Yb+, excites the ion reducing the phonon number by one. Second, laser light exciting the S1/2, F=1 ↔ P1/2, F=1 dipole allowed resonance pumps the ion back to the initial F=0 state but with a phonon less. The trap is characterized by an axial trapping frequency of 121 kHz. We systematically measure the final ion temperature for different microwave and laser intensities. For the optimized set of parameters we show a reduction of more than one order of magnitude on the mean phonon occupation number from ⟨ n ⟩ = 176 ± 30 to ⟨ n ⟩ = 4 ± 4 achieving temperatures close to the ground state.
[Show abstract][Hide abstract] ABSTRACT: We report on the experimental investigation of an individual pseudomolecule
using trapped ions with adjustable magnetically induced J-type coupling between
spin states. Resonances of individual spins are well separated and are
addressed with high fidelity. Quantum gates are carried out using microwave
radiation in the presence of thermal excitation of the pseudomolecule's
vibrations. Demonstrating Controlled-NOT gates between non-nearest neighbors
serves as a proof-of-principle of a quantum bus employing a spin chain.
Combining advantageous features of nuclear magnetic resonance experiments and
trapped ions, respectively, opens up a new avenue towards scalable quantum
Full-text · Article · Jun 2012 · Physical Review Letters
[Show abstract][Hide abstract] ABSTRACT: Already early on during the development of quantum information science nuclear magnetic resonance (NMR) has been successfully applied to realize quantum algorithms based on J-coupling between nuclear spins in molecules. Scalability of NMR is hampered mainly by the use of ensembles of molecules. Additionally, nuclear spin resonances and J-coupling between spins are determined by the molecule structure, and thus often are not well suited for quantum computing. Here, we report on the creation and experimental investigation of an individual 3-spin pseudo-molecule that exhibits adjustable J-type coupling between spin states. This coupling has been employed to entangle consecutive spins or distant ones at demand using microwave radiation. Effective spin-1/2 systems are realized by using hyperfine states of trapped atomic ions. They are addressed with high fidelity since the resonances of individual spins are well separated due to a spatially varying magnetic field which also induces the J-type coupling mediated by the vibrational modes of this ion pseudo-molecule. The demonstration of Conditional-NOT gates between non-nearest neighbours serves as a proof-of- principle of a novel quantum bus employing a spin chain.
[Show abstract][Hide abstract] ABSTRACT: Dynamical decoupling (DD) is a widely used technique in the framework of nuclear magnetic resonance to protect the coherence of quantum systems against a detrimental environment. DD pulse sequences can be used to enhance the coherence time of quantum memories and the fidelity of quantum gates. However, imperfections of pulses may destroy quantum information or interfere with gate dynamics. We investigate different sequences with respect to their capability to suppress decoherence while still being robust against pulse imperfections in an ion trap experiment. Our results obtained with 171Yb+ ions demonstrate that sequences based on varying phases are self-correcting. We found sequences that allow for the implementation of a conditional quantum gate even if the gate time is more than one order of magnitude longer than the coherence time of the system. Furthermore, we show that DD sequences can be combined with selective recoupling to implement quantum memories with trapped ions.
[Show abstract][Hide abstract] ABSTRACT: Trapped atomic ions have been used successfully to demonstrate basic elements of universal quantum information processing. Nevertheless, scaling up such methods to achieve large-scale, universal quantum information processing (or more specialized quantum simulations) remains challenging. The use of easily controllable and stable microwave sources, rather than complex laser systems, could remove obstacles to scalability. However, the microwave approach has drawbacks: it involves the use of magnetic-field-sensitive states, which shorten coherence times considerably, and requires large, stable magnetic field gradients. Here we show how to overcome both problems by using stationary atomic quantum states as qubits that are induced by microwave fields (that is, by dressing magnetic-field-sensitive states with microwave fields). This permits fast quantum logic, even in the presence of a small (effective) Lamb-Dicke parameter (and, therefore, moderate magnetic field gradients). We experimentally demonstrate the basic building blocks of this scheme, showing that the dressed states are long lived and that coherence times are increased by more than two orders of magnitude relative to those of bare magnetic-field-sensitive states. This improves the prospects of microwave-driven ion trap quantum information processing, and offers a route to extending coherence times in all systems that suffer from magnetic noise, such as neutral atoms, nitrogen-vacancy centres, quantum dots or circuit quantum electrodynamic systems.
[Show abstract][Hide abstract] ABSTRACT: Two 171Yb+ ions are electrodynamically trapped in presence of a magnetic gradient field. This magnetic field not only allows to address the ions independently  but also accounts for an effective spin-spin coupling . This interaction was measured in a linear Paul trap using spin echo techniques on Doppler-cooled ions.
The magnetic field gradient is produced by means of two permanent magnets with identical poles facing toward each other and reaches up to 17 T/m. Having the axial trap potentials in the range of hundred kilohertz we are able to measure coupling constants of a few tens of hertz. The measured values we obtained are in good agreement with the theoretical expectations.
[Show abstract][Hide abstract] ABSTRACT: The control of internal and motional quantum degrees of freedom of laser
cooled trapped ions has been subject to intense theoretical and experimental
research for about three decades. In the realm of quantum information science
the ability to deterministically prepare and measure quantum states of trapped
ions is unprecedented. This expertise may be employed to investigate physical
models conceived to describe systems that are not directly accessible for
experimental investigations. Here, we give an overview of current theoretical
proposals and experiments for such quantum simulations with trapped ions. This
includes various spin models (e.g., the quantum transverse Ising model, or a
neural network), the Bose-Hubbard Hamiltonian, the Frenkel-Kontorova model, and
quantum fields and relativistic effects.
Full-text · Article · Aug 2009 · Journal of Physics B Atomic Molecular and Optical Physics
[Show abstract][Hide abstract] ABSTRACT: In order to perform accurate spectroscopic measurements or to drive atomic transitions one requires to know precisely the wavelength of the lasers. In our lab we have built a Michelson based wavelength meter , which uses an atomic Rb transition as a reference .
With our wavelength meter we are able to measure the wavelengths in the range of 350 nm - 1µm - the range of the optical components. Using Labview we are able to choose between four different wavelengths that are simultaneously coupled into the wavelength meter.
The reference laser is a frequency-stabilized diode laser at 780 nm. It is locked to the cross-over signal (linewidth 6MHz) of the 52S1/2,F=2↔ 52P3/2,F=2 and F=3 transition in the 87Rb. The relative error on the unknown wavelength equals 10−8. Counter and electronics set the limits on the precision. The details of the set up and physical principles of the used techniques will be highlighted.