Laser cooling in the Penning trap: an analytical model for cooling rates in the presence of an axializing field (original) (raw)

Individual Addressing of Trapped Ions and Coupling of Motional and Spin States Using rf Radiation

Physical Review Letters, 2009

Individual electrodynamically trapped and laser cooled ions are addressed in frequency space using radio-frequency radiation in the presence of a static magnetic field gradient. In addition, an interaction between motional and spin states induced by an rf field is demonstrated employing rfoptical double resonance spectroscopy. These are two essential experimental steps towards realizing a novel concept for implementing quantum simulations and quantum computing with trapped ions.

Erratum: Ion-trap Quantum Logic Using Long-Wavelength Radiation

Physical Review Letters - PHYS REV LETT, 2003

A quantum information processor is proposed that combines experimental techniques and technology successfully demonstrated either in nuclear magnetic resonance experiments or with trapped ions. An additional inhomogenenous magnetic field applied to an ion trap i) shifts individual ionic resonances (qubits), making them distinguishable by frequency, and, ii) mediates the coupling between internal and external degrees of freedom of trapped ions. This scheme permits one to individually address and coherently manipulate ions confined in an electrodynamic trap using radiation in the radiofrequency or microwave regime. 03.67.Lx, 42.50.Vk Quantum information processing (QIP) holds the promise of extending today's computing capabilities to problems that, with increasing complexity, require exponentially growing resources in time and/or the number of physical elements . The computation of properties of quantum systems themselves is particularly suited to be performed on a quantum computer, even on a device where logic operations can only be carried out with limited precision . Elements of quantum logic operations have been successfully demonstrated in experiments using ion traps , cavity quantum electrodynamics and in the case of nuclear magnetic resonance (NMR) even algorithms have been performed . Whereas quantum computation with nuclear spins in macroscopic ensembles can most likely not be extended beyond about 10 qubits (quantum mechanical two-state systems) [8], ion traps do not suffer from limited scalability in principle and represent a promising system to explore QIP experimentally. They can be employed to also investigate fundamental questions of quantum physics, for example related to decoherence [9] or multiparticle entanglement . However, they still pose considerable experimental challenges.

Measurement of the secular motion frequency and the space charge density in the linear ion trap

Chinese Physics B, 2010

This paper reports that a cloud of laser-cooled 40 Ca + is successfully trapped and manipulated in the home-built linear ion trap constructed for quantum information processing (QIP). The frequency of the secular motion and the space charge density of the ion cloud are measured, which help knowing the characteristic of the trapping potential and are the prerequisite of QIP with the trapped ions.

Doppler cooling of Ca^{+} ions in a Penning trap

Physical Review A, 2004

We have laser cooled a small cloud of 40 Ca ϩ ions stored in a Penning trap. The large Zeeman splittings that result from the presence of the imposed magnetic field necessitate the use of two cooling lasers tuned to the 2 S 1/2-2 P 1/2 transition near 397 nm ͑whereas only a single blue laser frequency is required in an rf trap͒. The 397 nm radiation is provided by a pair of blue diode lasers operated in extended cavities. Ions can escape from the cooling cycle by falling into a 2 D 3/2 state. There is also a small probability that ions can be pumped into a 2 D 5/2 state. The presence of large Zeeman splittings complicates the provision of repumper radiation to empty the D states. We describe two repumping schemes. The first scheme employs five infrared extended cavity diode lasers ͑ECDL's͒. The second scheme employs three infrared ECDL's, two of which have their injection current modulated to produce sidebands. An upper bound to the temperature of 1 K is inferred from the linewidth of the 397-nm fluorescence for a small cloud of 40 Ca ϩ ions in our Penning trap. This work is part of a program aimed at using atomic ions in a Penning trap for decoherence studies and quantum information processing.

Tutorial review Cold trapped ions as quantum information processors

In this tutorial we review the physical implementation of quantum computing using a system of cold trapped ions. We discuss systematically all the aspects for making the implementation possible. Firstly, we go through the loading and con®ning of atomic ions in the linear Paul trap, then we describe the collective vibrational motion of trapped ions. Further, we discuss interactions of the ions with a laser beam. We treat the interactions in the travellingwave and standing-wave con®guration for dipole and quadrupole transitions. We review di erent types of laser cooling techniques associated with trapped ions. We address Doppler cooling, sideband cooling in and beyond the Lamb± Dicke limit, sympathetic cooling and laser cooling using electromagnetically induced transparency. After that we discuss the problem of state detection using the electron shelving method. Then quantum gates are described. We introduce single-qubit rotations, two-qubit controlled-NOT and multi-qubit controlled-NOT gates. We also comment on more advanced multiple-qubit logic gates. We describe how quantum logic networks may be used for the synthesis of arbitrary pure quantum states. Finally, we discuss the speed of quantum gates and we also give some numerical estimations for them. A discussion of dynamics on o -resonance transitions associated with a qualitative estimation of the weak-coupling regime is included in Appendix A and of the Lamb±Dicke regime in Appendix B.

Experiments towards quantum information with trapped Calcium ions

Arxiv preprint quant-ph/ …, 2000

Ground state cooling and coherent manipulation of ions in an rf-(Paul) trap is the prerequisite for quantum information experiments with trapped ions. With resolved sideband cooling on the optical S 1/2 -D 5/2 quadrupole transition we have cooled one and two 40 Ca + ions to the ground state of vibration with up to 99.9% probability. With a novel cooling scheme utilizing electromagnetically induced transparency on the S 1/2 -P 1/2 manifold we have achieved simultaneous ground state cooling of two motional sidebands 1.7 MHz apart. Starting from the motional ground state we have demonstrated coherent quantum state manipulation on the S 1/2 -D 5/2 quadrupole transition at 729 nm. Up to 30 Rabi oscillations within 1.4 ms have been observed in the motional ground state and in the n = 1 Fock state. In the linear quadrupole rf-trap with 700 kHz trap frequency along the symmetry axis (2 MHz in radial direction) the minimum ion spacing is more than 5 µm for up to 4 ions. We are able to cool two ions to the ground state in the trap and individually address the ions with laser pulses through a special optical addressing channel.

Ion dynamics in a linear radio-frequency trap with a single cooling laser

Physical Review A, 2010

We analyse the possibility of cooling ions with a single laser beam, due to the coupling between the three components of their motion induced by the Coulomb interaction. For this purpose, we numerically study the dynamics of ion clouds of up to 140 particles, trapped in a linear quadrupole potential and cooled with a laser beam propagating in the radial plane. We use Molecular Dynamics simulations and model the laser cooling by a stochastic process. For each component of the motion, we systematically study the dependence of the temperature with the anisotropy of the trapping potential. Results obtained using the full radio-frequency (rf) potential are compared to those of the corresponding pseudo-potential. In the rf case, the rotation symmetry of the potential has to be broken to keep ions inside the trap. Then, as for the pseudo-potential case, we show that the efficiency of the Coulomb coupling to thermalize the components of motion depends on the geometrical configuration of the cloud. Coulomb coupling appears to be not efficient when the ions organise as a line or a pancake and the three components of motion reach the same temperature only if the cloud extends in three dimensions.

Parametric excitations of trapped ions in a linear rf ion trap

Physical Review A, 2002

The parametric resonant behavior of ions inside a linear rf ion trap is studied both theoretically and experimentally. Theoretically, the resonant motion of ions inside an ideal ion trap is described by approximating the trapping rf field as a harmonic pseudopotential with the ions being excited by an additional quadrupolar ac voltage. The resulting damped Mathieu equation is studied and the regions of resonant instability are predicted by investigating the solutions. Experimentally, the parametric excitation of Mg ϩ ions is observed by subjecting the cloud of trapped ions to an additional quadrupolar ac field. The various ion motion resonances are detected through the disappearance of the laser-induced fluorescence signal. Weak damping is introduced by the presence of a low-pressure buffer gas. The experimental results are compared with the theoretical predictions.

Cold trapped ions as quantum information processors

Journal of Modern Optics, 2002

In this tutorial we review physical implementation of quantum computing using a system of cold trapped ions. We discuss systematically all the aspects for making the implementation possible. Firstly, we go through the loading and confining of atomic ions in the linear Paul trap, then we describe the collective vibrational motion of trapped ions. Further, we discuss interactions of the ions with a laser beam. We treat the interactions in the travelling-wave and standing-wave configuration for dipole and quadrupole transitions. We review different types of laser cooling techniques associated with trapped ions. We address Doppler cooling, sideband cooling in and beyond the Lamb-Dicke limit, sympathetic cooling and laser cooling using electromagnetically induced transparency. After that we discuss the problem of state detection using the electron shelving method. Then quantum gates are described. We introduce single-qubit rotations, two-qubit controlled-NOT and multi-qubit controlled-NOT gates. We also comment on more advanced multi-qubit logic gates. We describe how quantum logic networks may be used for the synthesis of arbitrary pure quantum states. Finally, we discuss the speed of quantum gates and we also give some numerical estimations for them. A discussion of dynamics on off-resonant transitions associated with a qualitative estimation of the weak coupling regime and of the Lamb-Dicke regime is included in Appendix.