Previous Research Highlights

2010

Summary

We extended the high fidelity measurement technique (see June 2008) to simultaneous detection of multiple qubits, using fluorescence imaging on a CCD array. The adaptive method is now based on spatial rather than temporal information.

We developed a technique to detect micromotion via its effect on a Raman transition. This enables us to use infra-red rather than ultra-violet beams to sense the motion. This is useful because ultra-violet radiation can destabilize the trap if it is allowed to strike the electrodes. We also measured heating rates and other characteristics of our planar trap (see March 2009), including an unusually high signal to background ratio for fluorescence detection from a surface trap.

Extending the lifetime of a qubit

We demonstrate the use of dynamic decoupling techniques to extend the coherence time of a single memory qubit by nearly two orders of magnitude. By extending the Hahn spin-echo technique to correct for unknown, arbitrary polynomial variations in the qubit precession frequency, we show analytically that the required sequence of π-pulses is identical to the Uhrig dynamic decoupling (UDD) sequence. We compare UDD and Carr–Purcell–Meiboom–Gill (CPMG) sequences applied to a single 43Ca+ trapped-ion qubit and find that they afford comparable protection in our ambient noise environment.

2009

Ions loaded into an Oxford microfabricated planar trap

We designed a planar trap array, based on gold on quartz fabrication. The ion-to-surface distance was 150 microns and typically vibrational frequency for trapped Ca ions is 3.5 MHz. Ions were successfully loaded into the trap array. Stability is under investigation. Initial observations give ion lifetime (with cooling) up to ~1 minute.

The fabrication method was developed in-house by D. Allcock, following the doctoral thesis of J. Labaziewicz (2008) from the MIT group.

Ion-surface distance 150 microns; rf drive 25 MHz, 200 V, trap depth 80 meV, radial secular frequency 3.5 MHz

2008

Fast high-fidelity readout of trapped ion qubits

We demonstrate single-shot qubit readout with a fidelity sufficient for fault-tolerant quantum computation. For an optical qubit stored in 40Ca we achieve 99.991(1)% average readout fidelity in one million trials, using time-resolved photon counting. An adaptive measurement technique allows 99.99% fidelity to be reached in 145 micro-second average detection time. For 43Ca, we propose and implement an optical pumping scheme to transfer a long-lived hyperfine qubit to the optical qubit, capable of a theoretical fidelity of 99.95% in 10 micro-sec. We achieve 99.87(4)% transfer fidelity and 99.77(3)% net readout fidelity.

Fidelities: Readout is achieved by driving the (S1/2 – P1/2 – D3/2) manifold and detecting the P1/2 – S1/2 fluorescence. Absence of fluorescence indicates that the qubit was in the metastable D5/2 state (lifetime 1168(7) ms).

2007

Heating rate measurement in microfabricated trap

Ions were successfully loaded into a 100 micron scale microfabricated trap array (manufactured by Sandia National Laboratories). Heating rate measurements were performed by a `wait and Doppler-cool' method. The observed value is at the upper end of the range previously reported for traps of this size.

Trap details: Tungsten on silicon, some Al (+oxide) coating, gold coat on backplane. 1 r.f. electrode pair and 14 d.c. electrodes around a 2mm x 0.4mm vacuum slot. Ion to electrode distance = 99.5 micron.

2006

March - High-quality readout and manipulation of Ca43 qubit

We measure a qubit stored in a single Ca43 ion, achieving 99% average single-shot readout accuracy. Driven rotation of the qubit by Rabi flopping gave 98% fringe amplitude.

Readout of Ca43 was achieved by state-selective shelving to D5/2 using alternating pulses of circularly polarized 393nm and linearly polarized 850nm light. After shelving, flourescence (of the non-shelved population) was observed. The shelving pulses took <1 ms, fluorescence detection 3 ms. Highly accurate single-shot measurement capability is crucial to quantum error correction and fault tolerant computing.

F=4, m =+4 was detected (i.e. counts < threshold) with P=0.977(2), F=3 was detected (i.e. counts > threshold) with P=0.9963(5).

We also observed Rabi flopping (see right). A fit to the raw flourescence readout data gives amplitude 94.4(6)%, frequency 9339(6)Hz. After scaling for the readout probabilities, this represents 97.8(8)% amplitude of the rotation of the qubit itself.

Ca43 qubit readout pulse sequence (top) and Rabi fringes (bottom)

April - Ultra-stable qubits

In a spin-echo experiment, we observe no detectable decoherence of a single Ca43 ion qubit after 1s. This implies T2 > 10s. The 2-qubit gate time in the same system is of order 10us, giving Q-parameter (memory coherence time divided by gate time) Q > 10^6.

Two spin-echo (pi/2,gap,pi,gap,pi/2) sequences were studied in an interleaved experiment, one (control) with a short gap, the other with a 0.5s gap. The Ramsey fringes had the same amplitude within experimental error. On an exponential model of fringe amplitude decay, we infer T2 > 100s; on a Gaussian model, T2 > 10s. The observed ratio of coherence time to 2-qubit gate time is among the highest observed to date in any system.

Spin echo sequence (top) and Ramsey fringes (bottom)

May - Sympathetic cooling to the motional ground state

An ion pair composed of one Ca40 ion and one Ca43 was cooled to the motional ground state by sideband cooling of the Ca40 ion only. The cooling was in one dimension, achieving 94% occupation of the ground state for both normal modes (centre of mass and stretch modes). The approx 1 GHz isotope shifts ensure the lasers interact almost exclusively with only one of the ions. This should allow a qubit to be stored and cooled in the other ion without decoherence.

Sympathetic Cooling: Observed red and blue sidebands of centre-of-mass and stretch modes

June - Qubit coherence preserved during cooling

A qubit was stored in one ion of a heterogeneous pair (in the Ca43 hyperfine state), while the motion of the pair was cooled using the other ion (see previous news item).

We measure the qubit coherence by a Ramsey experiment, while the motion is being actively cooled. Some decoherence is observed, but this is primarily due to a well-known source, photon scattering from the Raman cooling beams, and can be eliminanted by using a higher power laser (by increasing the detuning). Cooling of the motion while preserving qubit coherence is a central element in the "ion chip" concept for ion trap quantum computing.

Observed stretch mode excitation and Ramsey contrast as the ions are cooled

2005

February - Determininistic entanglement of two trapped ion spin qubits

We achieved the deterministic entanglement of two Calcium-40 ions in a Paul trap with 75(5)% fidelity.

Deterministic entanglement has previously been reported using beryllium ions (NIST, Boulder) and calcium ions (Innsbruck). This work differs from the latter in the method of gate operation and in the choice of internal states of calcium which realise the qubits: here each qubit is represented by the spin state of a calciun ion. The complete experimental sequence involves cooling the ions, the entangling "logic gate" operation implemented within a "spin-echo", and measurement of the final state. The entangling operation uses a 77 microsecond pulse from a pair of laser beams illuminating the pair of trapped ions (c.f. figure). The laser beams set up a standing wave pattern of light, and the ions experience a force which depends on their location in this standing wave. The force is made to oscillate near to a natural oscillation frequency of the ion pair, with the result that they first pick up and then lose motional energy in a beating effect. The laser pulse is switched off just as the state of motion returns to rest. The different motions experienced by different spin states of the ions result in different accumulated quantum phase. These phases can be tuned to result in the desired logic gate effect. When the spin-echo sequence is also included, the net effect is to produce the Bell state (|down,down>-i|up,up>)/sqrt(2) in an ideal experiment.

A pair of laser beams produce a spin-dependent oscillating force which is used to entangle a pair of ions

Top: Experimental sequence. Bottom: measured parity P(up-up)+P(down-down)-P(up-down)-P(down-up) as a function of rotation axis of the analysis pulse. This quantity cannot oscillate by more than +/- 0.5 for a non-entangled state.

To diagnose the outcome, we use a further analysis pulse to rotate the ion spins about a chosen axis, and then measure them. We thus obtain the parity P(up up) + P(down down) - P(up down) - P(down up) of the qubits. The peak to peak amplitude of the parity oscillation only exceeds one if the state prior to the analysis pulse is entangled, and permits a lower bound on the fidelity to be obtained. We obtain fidelity F > 75(5)%.

June - Tomography of entangled state of two ion qubits

We now achieve the deterministic entanglement of two Calcium-40 ions in a Paul trap with 82(2)% fidelity (c.f. previous news item).

We developed a tomography method to completely characterise the density matrix of sets of qubits, and applied it to entangled states. In the image on the right the heights of the bars represent the absolute value of the density matrix elements (in the basis up-up, up-down, down-up, down-down) and the pie diagrams on the off-diagonal elements give the phases. The "castle" shape is characteristic of an entangled state having all the population in the extreme states (up-up) and (down-down), with a healthy (i.e. large) value of the coherence between these cases.

Extracted density matrix

June - Very long (1 second) coherence time of a single qubit

We loaded single ions of the rare isotope Ca-43, and performed Rabi and Ramsey experiments using transitions within the ground state hyperfine structure, driven by 3.2 GHz microwave excitation. The coherence time of 0.9 +/- 0.1 second is observed on the F=3,M=0 to F=4,M=0 "clock" transition. (These are also the first ever experiments on single ions of this isotope.)

Coherence time of Ca-43 qubit measured using Ramsey experiment

2004

'Schrodinger cat' entangled spin/motion states up to alpha=3 observed

A single ion is driven into two different coherent motional states simultaneously, and then brought back together. The motional state is entangled with the internal spin state. The diagram on the right summarizes the motion by showing the two paths in phase space. On the left the dots are data, the line is a fitted curve. The data show the probability of observing spin "up" after an interference experiment. The fringe visibility disappears when the spin is entangled with the motion, but, crucially, reappears when the motional state is reconstructed, proving that a superposition not merely a probabilistic mixture was produced.

1D ground state cooling: single ions n = 0.1 and two-ion crystals n = (0.1, 0.75)

2003

First Rabi flops on a single spin-qubit

A single ion is driven into a superposition of two internal states by a resonant RF field.

First observation of laser-cooled trapped Ca-43 ions

Calcium-43 is a rare isotope (0.4% natural abundance) which is important to quantum computing experiments because it has non-zero nuclear spin and hence hyperfine structure. Previous work has observed the very narrow hyperfine resonance of the ground state using clouds of trapped Ca-43 ions. In this work small ion clouds were laser-cooled for the first time, allowing "Coulomb crystals", and in particular a well-located string of ions (see picture) to be observed. We were able to load this rare isotope from a natural (unenriched) source by an isotope-selective photoionisation method.

A string of nine Ca-43 ions in the trap. The figure shows the fluorescence from the ion string when it is illuminated by laser light at 397 nm wavelength. The image is from monochrome CCD camera - the false colour scales with intensity.

2002

Overhead and noise threshold of fault-tolerant quantum error correction

This theoretical paper provides a wide-ranging analysis of fault-tolerant methods for quantum error correction, and brings together a number of issues previously little studied. In particular, it is shown that by making error correcting networks more efficient, the threshold for memory noise is increased by around an order of magnitude.

High-Efficiency Detection of a Single Quantum of Angular Momentum by Suppression of Optical Pumping

The reliable detection of the spin state of a single spin-half particle is challenging but widely sought-after. It is relevent, for example, to quantum computing experiments in which qubits are stored in single spins. In this work we propose and demonstrate experimentally the discrimination between two spin states of an atom purely on the basis of their angular momentum. The discrimination relies on angular momentum selection rules and does not require magnetic effects such as a magnetic dipole moment of the atom or an applied magnetic field. The central ingredient is to prevent by coherent population trapping an optical pumping process which would otherwise relax the spin state before a detectable signal could be obtained. We detected the presence or absence of a single quantum (1 hbar) of angular momentum in a trapped calcium ion in a single observation with success probability 0.86.

Early years

2000 - Measurement of the lifetime of the 3d 2D_5/2 state in 40Ca+

We report the most precise measurement of a metastable lifetime in an alkali-like ion. We obtain tau = 1.168 +/- 0.007 s from observation of nearly 64 000 quantum jumps during 32 h

1999 - First loading of ions in the Oxford trap