arXiv subjects

R. Blatt

Publications and source records attributed to R. Blatt.

At least 73 records · Page 4Linked to original sources

arXiv2009

Deterministic entanglement of ions in thermal states of motion

We give a detailed description of the implementation of a Molmer-Sorensen gate entangling two Ca+ ions using a bichromatic laser beam near-resonant with a quadrupole transition. By amplitude pulse shaping and compensation of AC-Stark shifts we achieve a fast gate operation without compromising the error rate. Subjecting different input states to concatenations of up to 21 individual gate operations reveals Bell state fidelities above 0.80. In principle, the entangling gate does not require ground state cooling of the ions as long as the Lamb-Dicke criterion is fulfilled. We present the first experimental evidence for this claim and create Bell states with a fidelity of 0.974(1) for ions in a thermal state of motion with a mean phonon number of =20(2) in the mode coupling to the ions' internal states.

quant-ph↗

arXiv2009

Quantum simulation of the Dirac equation

The Dirac equation is a cornerstone in the history of physics, merging successfully quantum mechanics with special relativity, providing a natural description of the electron spin and predicting the existence of anti-matter. Furthermore, it is able to reproduce accurately the spectrum of the hydrogen atom and its realm, relativistic quantum mechanics, is considered as the natural transition to quantum field theory. However, the Dirac equation also predicts some peculiar effects such as Klein's paradox and Zitterbewegung, an unexpected quivering motion of a free relativistic quantum particle first examined by Schrödinger. These and other predictions would be difficult to observe in real particles, while constituting key fundamental examples to understand relativistic quantum effects. Recent years have seen an increased interest in simulations of relativistic quantum effects in different physical setups, where parameter tunability allows accessibility to different physical regimes. Here, we perform a proof-of-principle quantum simulation of the one-dimensional Dirac equation using a single trapped ion, which is set to behave as a free relativistic quantum particle. We measure as a function of time the particle position and study Zitterbewegung for different initial superpositions of positive and negative energy spinor states, as well as the cross-over from relativistic to nonrelativistic dynamics. The high level of control of trapped-ion experimental parameters makes it possible to simulate elegant textbook examples of relativistic quantum physics.

quant-ph↗

arXiv2009

High fidelity entanglement of 43Ca+ hyperfine clock states

In an experiment using the odd calcium isotope 43Ca+ we combine the merits of a high fidelity entangling operation on an optical transition (optical qubit) with the long coherence times of two 'clock' states in the hyperfine ground state (hyperfine qubit) by mapping between these two qubits. For state initialization, state detection, global qubit rotations and mapping operations, errors smaller than 1% are achieved whereas the entangling gate adds errors of 2.3%. Based on these operations, we create Bell states with a fidelity of 96.9(3)% in the optical qubit and a fidelity of 96.7(3)% when mapped to the hyperfine states. In the latter case, the entanglement is preserved for 96(3) ms, exceeding the duration of a single gate operation by three orders of magnitude.

quant-ph↗

arXiv2009

State-independent experimental test of quantum contextuality

The question of whether quantum phenomena can be explained by classical models with hidden variables is the subject of a long lasting debate. In 1964, Bell showed that certain types of classical models cannot explain the quantum mechanical predictions for specific states of distant particles. Along this line, some types of hidden variable models have been experimentally ruled out. An intuitive feature for classical models is non-contextuality: the property that any measurement has a value which is independent of other compatible measurements being carried out at the same time. However, the results of Kochen, Specker, and Bell show that non-contextuality is in conflict with quantum mechanics. The conflict resides in the structure of the theory and is independent of the properties of special states. It has been debated whether the Kochen-Specker theorem could be experimentally tested at all. Only recently, first tests of quantum contextuality have been proposed and undertaken with photons and neutrons. Yet these tests required the generation of special quantum states and left various loopholes open. Here, using trapped ions, we experimentally demonstrate a state-independent conflict with non-contextuality. The experiment is not subject to the detection loophole and we show that, despite imperfections and possible measurement disturbances, our results cannot be explained in non-contextual terms.

quant-ph↗

arXiv2009

Intensity-field correlation of single-atom resonance fluorescence

We report measurements of an intensity-field correlation function of the resonance fluorescence of a single trapped Ba+ ion. Detection of a photon prepares the atom in its ground state and we observe its subsequent evolution under interaction with a laser field of well defined phase. We record the regression of the resonance fluorescence source field. This provides a direct measurement of the field of the radiating dipole of a single atom and exhibits its strong non-classical behavior. In the experimental setup an interference measurement is conditioned on a fluorescence photon detection. The third-order correlation function thus recorded demonstrates an aspect of wave-particle duality at the single-atom, single-photon level.

quant-ph↗

arXiv2008

Raman spectroscopy of a single ion coupled to a high-finesse cavity

We describe an ion-based cavity-QED system in which the internal dynamics of an atom is coupled to the modes of an optical cavity by vacuum-stimulated Raman transitions. We observe Raman spectra for different excitation polarizations and find quantitative agreement with theoretical simulations. Residual motion of the ion introduces motional sidebands in the Raman spectrum and leads to ion delocalization. The system offers prospects for cavity-assisted resolved-sideband ground-state cooling and coherent manipulation of ions and photons.

quant-ph↗

arXiv2008

Precision measurement of the branching fractions of the 4P3/2 decay of Ca II

We perform precision measurements of the branching ratios of the 4P3/2 level decay of a single 40Ca+ ion suspended in a linear Paul trap. High precision is achieved by a novel technique based on monitoring the population transfer when repeatedly pumping the ion between different internal states. The branching fractions into the 4S1/2, 3D5/2 and 3D3/2 levels are found to be 0.9347(3), 0.0587(2) and 0.00661(4), respectively. For the branching ratio A(P3/2-S1/2)/\sum_J A(P3/2-D_J)=14.31(5), we find a forty-fold improvement in accuracy as compared to the best previous measurement.

physics.atom-ph↗

arXiv2008

Quantum interference from remotely trapped ions

We observe quantum interference of photons emitted by two continuously laser-excited single ions, independently trapped in distinct vacuum vessels. High contrast two-photon interference is observed in two experiments with different ion species, calcium and barium. Our experimental findings are quantitatively reproduced by Bloch equation calculations. In particular, we show that the coherence of the individual resonance fluorescence light field is determined from the observed interference.

quant-ph↗

arXiv2008

Quantum computing with trapped ions

Quantum computers hold the promise to solve certain computational task much more efficiently than classical computers. We review the recent experimental advancements towards a quantum computer with trapped ions. In particular, various implementations of qubits, quantum gates and some key experiments are discussed. Furthermore, we review some implementations of quantum algorithms such as a deterministic teleportation of quantum information and an error correction scheme.

quant-ph↗

arXiv2008

Absolute frequency measurement of the 40Ca+ S1/2 - D5/2 clock transition

We report on the first absolute transition frequency measurement at the 10^{-15} level with a single, laser-cooled 40Ca+ ion in a linear Paul trap. For this measurement, a frequency comb is referenced to the transportable Cs atomic fountain clock of LNE-SYRTE and is used to measure the S1/2-D5/2 electric-quadrupole transition frequency. After the correction of systematic shifts, the clock transition frequency f_Ca+ = 411 042 129 776 393.2 (1.0) Hz is obtained, which corresponds to a fractional uncertainty within a factor of three of the Cs standard. Future improvements are expected to lead to an uncertainty surpassing the best Cs fountain clocks. In addition, we determine the Lande g-factor of the D5/2 level to be gD5/2=1.2003340(3).

physics.atom-ph↗

arXiv2008

Experimental quantum information processing with 43Ca+ ions

For quantum information processing (QIP) with trapped ions, the isotope 43Ca+ offers the combined advantages of a quantum memory with long coherence time, a high fidelity read out and the possibility of performing two qubit gates on a quadrupole transition with a narrow-band laser. Compared to other ions used for quantum computing, 43Ca+ has a relatively complicated level structure. In this paper we discuss how to meet the basic requirements for QIP and demonstrate ground state cooling, robust state initialization and efficient read out for the hyperfine qubit with a single 43Ca+ ion. A microwave field and a Raman light field are used to drive qubit transitions, and the coherence times for both fields are compared. Phase errors due to interferometric instabilities in the Raman field generation do not limit the experiments on a time scale of 100 ms. We find a quantum information storage time of many seconds for the hyperfine qubit.

quant-ph↗

arXiv2008

Realization of the quantum Toffoli gate with trapped ions

Algorithms for quantum information processing are usually decomposed into sequences of quantum gate operations, most often realized with single- and two- qubit gates[1]. While such operations constitute a universal set for quantum computation, gates acting on more than two qubits can simplify the implementation of complex quantum algorithms[2]. Thus, a single three-qubit operation can replace a complex sequence of two-qubit gates, which in turn promises faster execution with potentially higher Fidelity. One important three-qubit operation is the quantum Toffoli gate which performs a NOT operation on a target qubit depending on the state of two control qubits. Here we present the first experimental realization of the quantum Toffoli gate in an ion trap quantum computer. Our implementation is particular effcient as we directly encode the relevant logic information in the motion of the ion string. [1] DiVincenzo, D. P. Two-bit gates are universal for quantum computation. cond-mat/9407022, Phys.Rev. A 51, 1015-1022 (1995). [2] Chiaverini, J. et al. Realization of quantum error correction. Nature 432, 602-605 (2004).

quant-ph↗

arXiv2008

Geometric phase gate on an optical transition for ion trap quantum computation

We propose a geometric phase gate of two ion qubits that are encoded in two levels linked by an optical dipole-forbidden transition. Compared to hyperfine geometric phase gates mediated by electric dipole transitions, the gate has many interesting properties, such as very low spontaneous emission rates, applicability to magnetic field insensitive states, and use of a co-propagating laser beam geometry. We estimate that current technology allows for infidelities of around 10$^{-4}$.

quant-ph↗

arXiv2008

Towards fault-tolerant quantum computing with trapped ions

Today ion traps are among the most promising physical systems for constructing a quantum device harnessing the computing power inherent in the laws of quantum physics. The standard circuit model of quantum computing requires a universal set of quantum logic gates for the implementation of arbitrary quantum operations. As in classical models of computation, quantum error correction techniques enable rectification of small imperfections in gate operations, thus allowing for perfect computation in the presence of noise. For fault-tolerant computation, it is commonly believed that error thresholds ranging between 10^-4 and 10^-2 will be required depending on the noise model and the computational overhead for realizing the quantum gates. Up to now, all experimental implementations have fallen short of these requirements. Here, we report on a Molmer-Sorensen type gate operation entangling ions with a fidelity of 99.3(1)% which together with single-qubit operations forms a universal set of quantum gates. The gate operation is performed on a pair of qubits encoded in two trapped calcium ions using a single amplitude-modulated laser beam interacting with both ions at the same time. A robust gate operation, mapping separable states onto maximally entangled states is achieved by adiabatically switching the laser-ion coupling on and off. We analyse the performance of a single gate and concatenations of up to 21 gate operations. The gate mechanism holds great promise not only for two-qubit but also for multi-qubit operations.

quant-ph↗

arXiv2007

Precision spectroscopy with two correlated atoms

We discuss techniques that allow for long coherence times in laser spectroscopy experiments with two trapped ions. We show that for this purpose not only entangled ions prepared in decoherence-free subspaces can be used but also a pair of ions that are not entangled but subject to the same kind of phase noise. We apply this technique to a measurement of the electric quadrupole moment of the 3d D5/2 state of 40Ca+ and to a measurement of the linewidth of an ultrastable laser exciting a pair of 40Ca+ ions.

quant-ph↗

arXiv2007

Nonlinear coupling of continuous variables at the single quantum level

We experimentally investigate nonlinear couplings between vibrational modes of strings of cold ions stored in linear ion traps. The nonlinearity is caused by the ions' Coulomb interaction and gives rise to a Kerr-type interaction Hamiltonian H = n_r*n_s, where n_r,n_s are phonon number operators of two interacting vibrational modes. We precisely measure the resulting oscillation frequency shift and observe a collapse and revival of the contrast in a Ramsey experiment. Implications for ion trap experiments aiming at high-fidelity quantum gate operations are discussed.

quant-ph↗

arXiv2007

Quantum teleportation with atoms: quantum process tomography

The performance of a quantum teleportation algorithm implemented on an ion trap quantum computer is investigated. First the algorithm is analyzed in terms of the teleportation fidelity of six input states evenly distributed over the Bloch sphere. Furthermore, a quantum process tomography of the teleportation algorithm is carried out which provides almost complete knowledge about the algorithm.

quant-ph↗

arXiv2007

Measurement of the hyperfine structure of the S1/2-D5/2 transition in 43Ca+

The hyperfine structure of the S1/2-D5/2 quadrupole transition at 729 nm in 43Ca+ has been investigated by laser spectroscopy using a single trapped 43Ca+ ion. We determine the hyperfine structure constants of the metastable level as A=-3.8931(2) MHz and B=-4.241(4) MHz. The isotope shift of the transition with respect to 40Ca+ was measured to be 4134.713(5) MHz. We demonstrate the existence of transitions that become independent of the first-order Zeeman shift at non-zero low magnetic fields. These transitions might be better suited for building a frequency standard than the well-known 'clock transitions' between m=0 levels at zero magnetic field.

physics.atom-ph↗