arXiv subjects

M. Riebe

Publications and source records attributed to M. Riebe.

15 recordsLinked to original sources

arXiv2009

Realization of Universal Ion Trap Quantum Computation with Decoherence Free Qubits

Any residual coupling of a quantum computer to the environment results in computational errors. Encoding quantum information in a so-called decoherence-free subspace provides means to avoid these errors. Despite tremendous progress in employing this technique to extend memory storage times by orders of magnitude, computation within such subspaces has been scarce. Here, we demonstrate the realization of a universal set of quantum gates acting on decoherence-free ion qubits. We combine these gates to realize the first controlled-NOT gate within a decoherence-free, scalable quantum computer.

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

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↗

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

'Designer atoms' for quantum metrology

Entanglement is recognized as a key resource for quantum computation and quantum cryptography. For quantum metrology, the use of entangled states has been discussed and demonstrated as a means of improving the signal-to-noise ratio. In addition, entangled states have been used in experiments for efficient quantum state detection and for the measurement of scattering lengths. In quantum information processing, manipulation of individual quantum bits allows for the tailored design of specific states that are insensitive to the detrimental influences of an environment. Such 'decoherence-free subspaces' protect quantum information and yield significantly enhanced coherence times. Here we use a decoherence-free subspace with specifically designed entangled states to demonstrate precision spectroscopy of a pair of trapped Ca+ ions; we obtain the electric quadrupole moment, which is of use for frequency standard applications. We find that entangled states are not only useful for enhancing the signal-to-noise ratio in frequency measurements - a suitably designed pair of atoms also allows clock measurements in the presence of strong technical noise. Our technique makes explicit use of non-locality as an entanglement property and provides an approach for 'designed' quantum metrology.

quant-ph↗

arXiv2006

Process tomography of ion trap quantum gates

A crucial building block for quantum information processing with trapped ions is a controlled-NOT quantum gate. In this paper, two different sequences of laser pulses implementing such a gate operation are analyzed using quantum process tomography. Fidelities of up to 92.6(6)% are achieved for single gate operations and up to 83.4(8)% for two concatenated gate operations. By process tomography we assess the performance of the gates for different experimental realizations and demonstrate the advantage of amplitude--shaped laser pulses over simple square pulses. We also investigate whether the performance of concatenated gates can be inferred from the analysis of the single gates.

quant-ph↗

arXiv2006

Scalable multi-particle entanglement of trapped ions

Among the various kinds of entangled states, the 'W state' plays an important role as its entanglement is maximally persistent and robust even under particle loss. Such states are central as a resource in quantum information processing and multiparty quantum communication. Here we report the scalable and deterministic generation of four-, five-, six-, seven- and eight-particle entangled states of the W type with trapped ions. We obtain the maximum possible information on these states by performing full characterization via state tomography, using individual control and detection of the ions. A detailed analysis proves that the entanglement is genuine. The availability of such multiparticle entangled states, together with full information in the form of their density matrices, creates a test-bed for theoretical studies of multiparticle entanglement. Independently, -Greenberger-Horne-Zeilinger- entangled states with up to six ions have been created and analysed in Boulder.

quant-ph↗

arXiv2005

Robust entanglement

It is common belief among physicists that entangled states of quantum systems loose their coherence rather quickly. The reason is that any interaction with the environment which distinguishes between the entangled sub-systems collapses the quantum state. Here we investigate entangled states of two trapped Ca$^+$ ions and observe robust entanglement lasting for more than 20 seconds.

quant-ph↗

arXiv2003

How to realize a universal quantum gate with trapped ions

We report the realization of an elementary quantum processor based on a linear crystal of trapped ions. Each ion serves as a quantum bit (qubit) to store the quantum information in long lived electronic states. We present the realization of single-qubit and of universal two-qubit logic gates. The qwo-qubit operation relies on the coupling of the ions through their collective quantized motion. A detailed description of the setup and the methods is included.

quant-ph↗

arXiv2003

Tomography of entangled massive particles

We report on tomographic means to study the stability of a qubit register based on a string of trapped ions. In our experiment, two ions are held in a linear Paul trap and are entangled deterministically by laser pulses that couple their electronic and motional states. We reconstruct the density matrix using single qubit rotations and subsequent measurements with near-unity detection efficiency. This way, we characterize the created Bell states, the states into which they subsequently decay, and we derive their entanglement, applying different entanglement measures.

quant-ph↗

arXiv2003

Quantized phase shifts and a dispersive universal quantum gate

A single 40Ca+ ion is trapped and laser cooled to its motional ground state. Laser radiation which couples off-resonantly to a motional sideband of the ion's S1/2 to D5/2 transition causes a phase shift proportional to the ion's motional quantum state |n>. As the phase shift is conditional upon the ion's motion, we are able to demonstrate a universal 2-qubit quantum gate operation where the electronic target state {S,D} is flipped depending on the motional qubit state |n>={|0>,|1>}. Finally, we discuss scaling properties of this universal quantum gate for linear ion crystals and present numerical simulations for the generation of a maximally entangled state of five ions.

quant-ph↗

arXiv2002

Precision measurement and compensation of optical Stark shifts for an ion-trap quantum processor

Using optical Ramsey interferometry, we precisely measure the laser-induced AC-stark shift on the $S_{1/2}$ -- $D_{5/2}$ "quantum bit" transition near 729 nm in a single trapped $^{40}$Ca$^+$ ion. We cancel this shift using an additional laser field. This technique is of particular importance for the implementation of quantum information processing with cold trapped ions. As a simple application we measure the atomic phase evolution during a $n \times 2π$ rotation of the quantum bit.

physics.atom-ph↗

arXiv2002

Coherence of qubits based on single Ca$^+$ ions

Two-level ionic systems, where quantum information is encoded in long lived states (qubits), are discussed extensively for quantum information processing. We present a collection of measurements which characterize the stability of a qubit based on the $S_{1/2}$--$D_{5/2}$ transition of single $^{40}$Ca$^+$ ions in a linear Paul trap. We find coherence times of $\simeq$1 ms, discuss the main technical limitations and outline possible improvements.

quant-ph↗