We demonstrate experimentally a robust quantum memory using a magnetic-field-independent hyperfine transition in 9 Be + atomic ion qubits at a magnetic field B ≃ 0.01194 T. We observe that the single physical qubit memory coherence time is greater than 10 seconds, an improvement of approximately five orders of magnitude from previous experiments with 9 Be + . We also observe long coherence times of decoherence-free subspace logical qubits comprising two entangled physical qubits and discuss the merits of each type of qubit.PACS numbers: 03.67. Pp, 32.60.+i, 03.65.Yz, 03.67.Mn Scalable quantum information processing (QIP) requires physical systems capable of reliably storing coherent superpositions for periods over which quantum error correction can be implemented [1]. Moreover, suppressing memory error rates to very low levels allows for simpler error-correcting algorithms [2,3]. In many current atomic ion QIP experiments, a dominant source of memory error is decoherence induced by fluctuating ambient magnetic fields [4,5]. To address this problem, we investigate creating long-lived qubit memories using a first-order magnetic-field-independent hyperfine transition and logical qubits of a decoherence-free subspace [6].Atomic systems have proven themselves as good candidates for quantum information storage through their use in highly stable atomic clocks [7]. Here, the principle of using first-order magnetic-field-independent transitions is well established. A typical clock transition |F, m F = 0 ↔ |F ′ , m F ′ = 0 between hyperfine states of angular momentum F and F ′ in alkali atoms has no linear Zeeman shift at zero magnetic field, and coherence times exceeding 10 minutes have been observed [8]. Unfortunately, magnetic sublevels in each hyperfine manifold are degenerate at zero magnetic field. This makes it more advantageous to operate at a nonzero field in order to spectrally resolve the levels, thereby inducing a linear field dependence of the transition frequency. However, field-independent transitions between hyperfine states also exist at nonzero magnetic field. In the context of atomic clocks, coherence times exceeding 10 minutes have been observed in 9 Be + ions at a magnetic field B = 0.8194 T [9].In neutral-atom systems suitable for QIP, fieldindependent transitions at nonzero magnetic field have been investigated in rubidium [10,11]. The radio-frequency (RF)/microwave two-photon stimulatedRaman hyperfine transition |F = 1, m F = −1 ↔ |F ′ = 2, m F ′ = 1 is field-independent at approximately 3.23 × 10 −4 T , and coherence times of 2.8 s have been observed [11]. In these and the clock experiments, transitions were driven by microwave fields on large numbers of atoms. Using microwaves, it may be difficult to localize the fields well enough to drive individual qubits unless a means (e.g., a magnetic-field gradient or Stark-shift gradient) is employed to provide spectral selection [12,13], a technique that has the additional overhead of keeping track of the phases induced by these shifts. With transitio...

We have investigated ion dynamics associated with a dual linear ion trap where ions can be stored in and moved between two distinct locations. Such a trap is a building block for a system to engineer arbitrary quantum states of ion ensembles. Specifically, this trap is the unit cell in a strategy for scalable quantum computing using a series of interconnected ion traps. We have transferred an ion between trap locations 1.2 mm apart in 50 $\mu$s with near unit efficiency ($> 10^{6}$ consecutive transfers) and negligible motional heating, while maintaining internal-state coherence. In addition, we have separated two ions held in a common trap into two distinct traps.

The coherence of a hyperfine-state superposition of a trapped 9 Be + ion in the presence of offresonant light is experimentally studied. It is shown that Rayleigh elastic scattering of photons that does not change state populations also does not affect coherence. Coherence times exceeding the average scattering time of 19 photons are observed. This result implies that, with sufficient control over its parameters, laser light can be used to manipulate hyperfine-state superpositions with very little decoherence.PACS numbers: 03.65. Yz, 03.65.Ta, 42.50.Ct Superpositions of hyperfine states of atoms have been the subject of considerable experimental interest. A good example is the role they have played in the development of atomic clocks over the last five decades [1]. More recently, hyperfine coherences of quantum-degenerate gases have been used to reveal their intrinsic properties [2,3]. Atomic hyperfine-state superpositions are also being investigated as possible information carriers for quantum information processing [4].In many such experiments, laser light is used to coherently manipulate the hyperfine superpositions with stimulated Raman transitions. In addition, laser light can be used to trap atoms as in the case of optical-dipole traps. Since light perturbs the energies of hyperfine levels, imperfect control of laser-beam parameters can lead to dephasing of the superpositions and loss of coherence [5,6,7].Past experiments with neutral-atoms in dipole traps investigated the coherence of hyperfine superpositions in the presence of light [6,7]. In these experiments the dominant source of dephasing was noise in experimental parameters such as fluctuations in the laser intensity or the ambient magnetic field.A more fundamental source of decoherence arises from spontaneous scattering of photons [8]. Spontaneous scattering is typically suppressed by detuning the laser frequency from allowed optical transitions, but it cannot be eliminated completely. Generally, if a spontaneously scattered photon carries information about which hyperfine state scattered the light, the event effectively measures the atomic state and the superposition collapses. In contrast, if the scattered photon does not contain this information then coherence is preserved. In this letter, we verify this effect by means of an experimental study of the hyperfine decoherence of a trapped 9 Be + ion caused by spontaneous scattering of photons from a non-resonant laser beam. Our results show that coherence can be preserved in the presence of spontaneous photon scattering.Off-resonant spontaneous scattering is a two-photon process in which the atom scatters a laser photon into an electromagnetic vacuum mode. Following such a scattering event the atom can be found in the same or a different internal state, corresponding to elastic Rayleigh or inelastic Raman scattering, respectively. The polarization and frequency of a Raman scattered photon depend on the angular momentum and energy imparted to the atom and are therefore entangled with the atomic i...

We show how an experimentally realized set of operations on a single trapped ion is sufficient to simulate a wide class of Hamiltonians of a spin-1/2 particle in an external potential. This system is also able to simulate other physical dynamics. As a demonstration, we simulate the action of an n-th order nonlinear optical beamsplitter. Two of these beamsplitters can be used to construct an interferometer sensitive to phase shifts in one of the interferometer beam paths. The sensitivity in determining these phase shifts increases linearly with n, and the simulation demonstrates that the use of nonlinear beamsplitters (n=2,3) enhances this sensitivity compared to the standard quantum limit imposed by a linear beamsplitter (n=1).One of the motivations behind Feynman's proposal for a quantum computer [1] was the possibility that one quantum system could efficiently simulate the behavior of other quantum systems. This idea was verified by Lloyd [2] and further explored by Lloyd and Braunstein [3] for a conjugate pair of variables such as position and momentum of a quantum particle. Following this suggestion we show below that coherent manipulation of the quantized motional and internal states of a single trapped ion using laser pulses can simulate the more general quantum dynamics of a single spin-1/2 particle in an arbitrary external potential. Previously, harmonic and anharmonic oscillators have been simulated in NMR [4].In addition to demonstrating the basic building blocks for simulating such arbitrary dynamics, we experimentally simulated the action of optical Mach-Zehnder interferometers with linear and nonlinear second-and thirdorder beam-splitters on number-states. Interferometers with linear beamsplitters and nonclassical input states have engendered considerable interest, since their noise limits for phase estimation can lie below the standard quantum limit for linear interferometers with coherent input modes [5][6][7][8] as has been demonstrated in experiments [9]. A number of optics experiments have exploited the second-order process of spontaneous parametric downconversion [10], which can be regarded as a nonlinear beamsplitter. By cascading this process, a fourth-order interaction has also recently been realized [11]. One difficulty in these experiments is the exponential decrease in efficiency as the order increases, necessitating data postselection and long integration times. In the simulations reported here, nonlinear interactions were implemented with high efficiency, eliminating the need for data postselection and thereby requiring relatively short integration times.To realize a quantum computer for simulating a spin s = 1/2 particle of mass µ in an arbitrary potential, one must be able to prepare an arbitrary input statewhere the particle's position wavefunction is expanded in energy eigenstates |n of a suitable harmonic oscillator and |m s (m s ∈ {↓, ↑}) represent the spin eigenstates in a suitable basis. We have recently demonstrated a method to generate arbitrary states of the type in Eq. (1)...

Atomic magnetometers have very high absolute precision and sensitivity to magnetic fields but suffer from a fundamental problem: the vectorial or tensorial interaction of light with atoms leads to "dead zones," certain orientations of the magnetic field where the magnetometer loses its sensitivity. We demonstrate a simple polarization modulation scheme that simultaneously creates coherent population trapping (CPT) in orientation and alignment, thereby eliminating dead zones. Using 87Rb in a 10 Torr buffer gas cell we measure narrow, high-contrast CPT transparency peaks for all orientations and also show the absence of systematic effects associated with nonlinear Zeeman splitting.