Jason M. Amini

Microwave quantum logic gates for trapped ions

Control over physical systems at the quantum level is important in fields as diverse as metrology, information processing, simulation and chemistry. For trapped atomic ions, the quantized motional and internal degrees of freedom can be coherently manipulated with laser light. Similar control is difficult to achieve with radio-frequency or microwave radiation: the essential coupling between internal degrees of freedom and motion requires significant field changes over the extent of the atoms’ motion, but such changes are negligible at these frequencies for freely propagating fields. An exception is in the near field of microwave currents in structures smaller than the free-space wavelength, where stronger gradients can be generated. Here we first manipulate coherently (on timescales of 20 nanoseconds) the internal quantum states of ions held in a microfabricated trap. The controlling magnetic fields are generated by microwave currents in electrodes that are integrated into the trap structure. We also generate entanglement between the internal degrees of freedom of two atoms with a gate operation suitable for general quantum computation; the entangled state has a fidelity of 0.76(3), where the uncertainty denotes standard error of the mean. Our approach, which involves integrating the quantum control mechanism into the trapping device in a scalable manner, could be applied to quantum information processing, simulation and spectroscopy.

Complete Methods Set for Scalable Ion Trap Quantum Information Processing

Hi Fi Quantum Computing In quantum information processing, one goal is to control the entangled states of objects such that they can interact during logical operations but otherwise have minimal interactions with their environment. In one scheme for quantum computing, ions are trapped within and physically moved by electric fields. One drawback is that the entangled states can be sensitive to stray magnetic fields. Home et al. (p. 1227, published online 6 August 2009) show that coupling of the ions (in this case, 9Be+) with a second ion (24Mg+) can create states that are relatively insensitive to magnetic fields and also allows for recooling of the ions during operation. This approach can minimize the loss of fidelity that occurs during ion transport. Coupling of different ions creates states that are insensitive to stray magnetic fields and more robust for quantum computing. Large-scale quantum information processors must be able to transport and maintain quantum information and repeatedly perform logical operations. Here, we show a combination of all of the fundamental elements required to perform scalable quantum computing through the use of qubits stored in the internal states of trapped atomic ions. We quantified the repeatability of a multiple-qubit operation and observed no loss of performance despite qubit transport over macroscopic distances. Key to these results is the use of different pairs of 9Be+ hyperfine states for robust qubit storage, readout, and gates, and simultaneous trapping of 24Mg+ “re-cooling” ions along with the qubit ions.

Entangled mechanical oscillators

Hallmarks of quantum mechanics include superposition and entanglement. In the context of large complex systems, these features should lead to situations as envisaged in the ‘Schrödinger’s cat’ thought experiment (where the cat exists in a superposition of alive and dead states entangled with a radioactive nucleus). Such situations are not observed in nature. This may be simply due to our inability to sufficiently isolate the system of interest from the surrounding environment—a technical limitation. Another possibility is some as-yet-undiscovered mechanism that prevents the formation of macroscopic entangled states. Such a limitation might depend on the number of elementary constituents in the system or on the types of degrees of freedom that are entangled. Tests of the latter possibility have been made with photons, atoms and condensed matter devices. One system ubiquitous to nature where entanglement has not been previously demonstrated consists of distinct mechanical oscillators. Here we demonstrate deterministic entanglement of separated mechanical oscillators, consisting of the vibrational states of two pairs of atomic ions held in different locations. We also demonstrate entanglement of the internal states of an atomic ion with a distant mechanical oscillator. These results show quantum entanglement in a degree of freedom that pervades the classical world. Such experiments may lead to the generation of entangled states of larger-scale mechanical oscillators, and offer possibilities for testing non-locality with mesoscopic systems. In addition, the control developed here is an important ingredient for scaling-up quantum information processing with trapped atomic ions.

Trapped-ion quantum logic gates based on oscillating magnetic fields.

Oscillating magnetic fields and field gradients can be used to implement single-qubit rotations and entangling multiqubit quantum gates for trapped-ion quantum information processing (QIP). With fields generated by currents in microfabricated surface-electrode traps, it should be possible to achieve gate speeds that are comparable to those of optically induced gates for realistic distances between the ion crystal and the electrode surface. Magnetic-field-mediated gates have the potential to significantly reduce the overhead in laser-beam control and motional-state initialization compared to current QIP experiments with trapped ions and will eliminate spontaneous scattering, a fundamental source of decoherence in laser-mediated gates.

Realization of a programmable two-qubit quantum processor

A simple programmable quantum processor has been created using trapped atomic ions. The system can be programmed with 15 classical inputs to produce any unitary operation on two qubits. This trapped-ion approach is amenable to scaling up for creating more complex circuits.

High precision measurement of the static dipole polarizability of cesium

The cesium 6(2)S(1/2) scalar dipole polarizability alpha(0) has been determined from the time-of-flight of laser cooled and launched cesium atoms traveling through an electric field. We find alpha(0)=6.611+/-0.009 x 10(-39) C m(2)/V=59.42+/-0.08 x 10(-24) cm(3)=401.0+/-0.6a(3)(0). The 0.14% uncertainty is a factor of 14 improvement over the previous measurement. Values for the 6(2)P(1/2) and 6(2)P(3/2) lifetimes and the 6(2)S(1/2) cesium-cesium dispersion coefficient C6 are determined from alpha(0) using the procedure of Derevianko and Porsev [Phys. Rev. A 65, 053403 (2002)]].

Simplified motional heating rate measurements of trapped ions

We have measured motional heating rates of trapped atomic ions, a factor that can influence multi-ion quantum logic gate fidelities. Two simplified techniques were developed for this purpose: one relies on Raman sideband detection implemented with a single laser source, while the second is even simpler and is based on time-resolved fluorescence detection during Doppler recooling. We applied these methods to determine heating rates in a microfrabricated surface-electrode trap made of gold on fused quartz, which traps ions 40 {mu}m above its surface. Heating rates obtained from the two techniques were found to be in reasonable agreement. In addition, the trap gives rise to a heating rate of 300{+-}30 s{sup -1} for a motional frequency of 5.25 MHz, substantially below the trend observed in other traps.

Efficient fiber optic detection of trapped ion fluorescence.

Integration of fiber optics may play a critical role in the development of quantum information processors based on trapped ions and atoms by enabling scalable collection and delivery of light and coupling trapped ions to optical microcavities. We trap 24Mg+ ions in a surface-electrode Paul trap that includes an integrated optical fiber for detecting 280-nm fluorescence photons. The collection numerical aperture is 0.37, and total collection efficiency is 2.1%. The ion can be positioned between 80 and 100 μm from the tip of the fiber by use of an adjustable rf pseudopotential.

Demonstration of integrated microscale optics in surface-electrode ion traps

In ion trap quantum information processing, efficient fluorescence collection is critical for fast, high-fidelity qubit detection and ion–photon entanglement. The expected size of future many-ion processors requires scalable light collection systems. We report on the development and testing of a microfabricated surface-electrode ion trap with an integrated high-numerical aperture (NA) micromirror for fluorescence collection. When coupled to a low-NA lens, the optical system is inherently scalable to large arrays of mirrors in a single device. We demonstrate the stable trapping and transport of 40Ca+ ions over a 0.63 NA micromirror and observe a factor of 1.9 enhancement of photon collection compared to the planar region of the trap.

Reliable transport through a microfabricated X-junction surface-electrode ion trap

We report the design, fabrication and characterization of a micro- fabricated surface-electrode ion trap that supports controlled transport through the two-dimensional intersection of linear trapping zones arranged in a 90 cross. The trap is fabricated with very large scalable integration techniques which are compatible with scaling to a large quantum information processor. The shape of the radio-frequency electrodes is optimized with a genetic algorithm to reduce axial pseudopotential barriers and minimize ion heating during transport. Seventy-eight independent dc control electrodes enable fine control of the trapping potentials. We demonstrate reliable ion transport between junction legs and determine the rate of ion loss due to transport. Doppler-cooled ions survive more than 10 5 round-trip transits between junction legs without loss and more than 65 consecutive round trips without laser cooling.