Displacement operators: the classical face of their quantum phase

In quantum mechanics, the operator representing the displacement of a system in position or momentum is always accompanied by a path-dependent phase factor. In particular, two non-parallel displacements in phase space do not compose together in a simple way, and the order of these displacements leads to different displacement composition phase factors. These phase factors are often attributed to the nonzero commutator between quantum position and momentum operators, but such a mathematical explanation might be unsatisfactory to students who are after more physical insight. We present a couple of simple demonstrations, using classical wave mechanics and classical particle mechanics, that provide some physical intuition for the phase associated with displacement operators.Comment: 14 pages, 4 figures, reorganized and reformatte

Spectroscopy of a synthetic trapped ion qubit

$^{133}\text{Ba}^+$ has been identified as an attractive ion for quantum information processing due to the unique combination of its spin-1/2 nucleus and visible wavelength electronic transitions. Using a microgram source of radioactive material, we trap and laser-cool the synthetic $A$ = 133 radioisotope of barium II in a radio-frequency ion trap. Using the same, single trapped atom, we measure the isotope shifts and hyperfine structure of the $6^2 \text{P}_{1/2}$ $\leftrightarrow$ $6^2 \text{S}_{1/2}$ and $6^2 \text{P}_{1/2}$ $\leftrightarrow$ $5^2 \text{D}_{3/2}$ electronic transitions that are needed for laser cooling, state preparation, and state detection of the clock-state hyperfine and optical qubits. We also report the $6^2 \text{P}_{1/2}$ $\leftrightarrow$ $5^2 \text{D}_{3/2}$ electronic transition isotope shift for the rare $A$ = 130 and 132 barium nuclides, completing the spectroscopic characterization necessary for laser cooling all long-lived barium II isotopes

Time-Domain Measurement of Spontaneous Vibrational Decay of Magnetically Trapped NH

The v = 1 -> 0 radiative lifetime of NH (X triplet-Sigma-, v=1,N=0) is determined to be tau_rad,exp. = 37.0 +/- 0.5 stat +2.0 / -0.8 sys miliseconds, corresponding to a transition dipole moment of |mu_10| = 0.0540 + 0.0009 / -0.0018 Debye. To achieve the long observation times necessary for direct time-domain measurement, vibrationally excited NH (X triplet-Sigma-, v=1,N=0) radicals are magnetically trapped using helium buffer-gas loading. Simultaneous trapping and lifetime measurement of both the NH(v=1, N=0) and NH(v=0,N=0) populations allows for accurate extraction of tau_rad,exp. Background helium atoms are present during our measurement of tau_rad,exp., and the rate constant for helium atom induced collisional quenching of NH(v=1,N=0) was determined to be k_q < 3.9 * 10^-15 cm^3/s. This bound on k_q yields the quoted systematic uncertainty on tau_rad,exp. Using an ab initio dipole moment function and an RKR potential, we also determine a theoretical value of 36.99 ms for this lifetime, in agreement with our experimental value. Our results provide an independent determination of tau_rad,10, test molecular theory, and furthermore demonstrate the efficacy of buffer-gas loading and trapping in determining metastable radiative and collisional lifetimes.Comment: 10 pages + 3 figures (11 pages total) v2 has minor corrections and explanations accepted for publication in PR

Polyqubit quantum processing

We describe the encoding of multiple qubits per atom in trapped atom quantum processors and methods for performing both intra- and inter-atomic gates on participant qubits without disturbing the spectator qubits stored in the same atoms. We also introduce techniques for selective state preparation and measurement of individual qubits that leave the information encoded in the other qubits intact, a capability required for qubit quantum error correction. The additional internal states needed for polyqubit processing are already present in atomic processors, suggesting that the resource cost associated with this multiplicative increase in qubit number could be a good bargain in the short to medium term.Comment: 9 pages, 4 figure

Dipole-phonon quantum logic with trapped polar molecular ions

The interaction between the electric dipole moment of a trapped molecular ion and the configuration of the confined Coulomb crystal couples the orientation of the molecule to its motion. We consider the practical feasibility of harnessing this interaction to initialize, process, and read out quantum information encoded in molecular ion qubits without optically illuminating the molecules. We present two schemes wherein a molecular ion can be entangled with a co-trapped atomic ion qubit, providing, among other things, a means for molecular state preparation and measurement. We also show that virtual phonon exchange can significantly boost range of the intermolecular dipole-dipole interaction, allowing strong coupling between widely-separated molecular ion qubits

Magnetic trapping and Zeeman relaxation of imidogen (NH X-triplet-Sigma)

Imidogen (NH) radicals are magnetically trapped and their Zeeman relaxation and energy transport collision cross sections with helium are measured. Continuous buffer-gas loading of the trap is direct from a room-temperature molecular beam. The Zeeman relaxation (inelastic) cross section of magnetically trapped electronic, vibrational and rotational ground state imidogen in collisions with He-3 is measured to be 3.8 +/- 1.1 E-19 cm^2 at 710 mK. The NH-He energy transport cross section is also measured, indicating a ratio of diffusive to inelastic cross sections of gamma = 7 E4 in agreement with the recent theory of Krems et al. (PRA 68 051401(R) (2003))Comment: 12 pages, 3 figure

Phonon lasing from optical frequency comb illumination of a trapped ion

An atomic transition can be addressed by a single tooth of an optical frequency comb if the excited state lifetime ($\tau$) is significantly longer than the pulse repetition period ($T_\mathrm{r}$). In the crossover regime between fully-resolved and unresolved comb teeth ($\tau \lessapprox T_\mathrm{r}$), we observe Doppler cooling of a pre-cooled trapped atomic ion by a single tooth of a frequency-doubled optical frequency comb. We find that for initially hot ions, a multi-tooth effect gives rise to lasing of the ion's harmonic motion in the trap, verified by acoustic injection locking. The gain saturation of this phonon laser action leads to a comb of steady-state oscillation amplitudes, allowing hot ions to be loaded directly into the trap and laser cooled to crystallization despite the presence of hundreds of blue-detuned teeth.Comment: 5 pages, 4 figure