News Archive
Oxford Ion Trap Group News
The Ion Trap Group at Oxford reports on three exciting news items:
June 2005 - 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 3.2GHz microwave excitation. The coherence time of 0.9(2)sec is observed on the F=3,M=0 to F=4,M=0 "clock" transition, and is about one thousand times longer than the coherence times observed in previous physical qubits based on calcium ions. (These are also the first ever experiments on single ions of this isotope.)
The picture shows Ramsey fringes (black curve) which measure the qubit coherence after a 300ms delay, compared with the coherence level after a very short delay (red dashed line). The small reduction in the amplitude of the Ramsey fringes demonstrates the long coherence time of the qubit.
June 2005 - 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. February 2005 news item).
Extracted density matrix.
We developed a tomography method to completely characterise the density matrix of sets of qubits, and applied it to entangled states. In the image above 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.
February 2005 - 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.
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)%.
(Andrew Steane, September 2005)
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