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Estimation of a general time-dependent Hamiltonian for a single qubit.

de Clercq LE, Oswald R, Flühmann C, Keitch B, Kienzler D, Lo HY, Marinelli M, Nadlinger D, Negnevitsky V, Home JP - Nat Commun (2016)

Bottom Line: The initially unknown Hamiltonian arises from transporting an ion through a static laser beam.Hamiltonian estimation allows us to estimate the spatial beam intensity profile and the ion velocity as a function of time.The estimation technique is general enough that it can be applied to other quantum systems, aiding the pursuit of high-operational fidelities in quantum control.

View Article: PubMed Central - PubMed

Affiliation: Institute for Quantum Electronics, ETH Zürich, Otto-Stern-Weg 1, 8093 Zürich, Switzerland.

ABSTRACT
The Hamiltonian of a closed quantum system governs its complete time evolution. While Hamiltonians with time-variation in a single basis can be recovered using a variety of methods, for more general Hamiltonians the presence of non-commuting terms complicates the reconstruction. Here using a single trapped ion, we propose and experimentally demonstrate a method for estimating a time-dependent Hamiltonian of a single qubit. We measure the time evolution of the qubit in a fixed basis as a function of a time-independent offset term added to the Hamiltonian. The initially unknown Hamiltonian arises from transporting an ion through a static laser beam. Hamiltonian estimation allows us to estimate the spatial beam intensity profile and the ion velocity as a function of time. The estimation technique is general enough that it can be applied to other quantum systems, aiding the pursuit of high-operational fidelities in quantum control.

No MeSH data available.


Related in: MedlinePlus

Experimental sequence and timing.(a) The experiment is carried out in three zones of the trap indicated by A, B and C. (b) The experimental sequence involves steps (i) through (v). Preparation and readout are carried out on the static ion in zone B. The qubit evolves while the ion is transported through the laser beam in zone B in a transport operation taking the ion from zone A to zone C. (c) Experimental sequence showing the timing of applied laser beams and ion transport, including shutting off the laser beam during transport.
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f1: Experimental sequence and timing.(a) The experiment is carried out in three zones of the trap indicated by A, B and C. (b) The experimental sequence involves steps (i) through (v). Preparation and readout are carried out on the static ion in zone B. The qubit evolves while the ion is transported through the laser beam in zone B in a transport operation taking the ion from zone A to zone C. (c) Experimental sequence showing the timing of applied laser beams and ion transport, including shutting off the laser beam during transport.

Mentions: The experimental sequence is depicted in Fig. 1. We start in zone B by cooling all motional modes of the ion to using a combination of Doppler and electromagnetically induced transparency cooling23, and then initialize the internal state by optical pumping into . The ion is then transported to zone A, and the laser beam used to implement the Hamiltonian is turned on in zone B. The ion is then transported through this laser beam to zone C. During the passage through the laser beam, we rapidly turn the beam off at time toff and thus stop the qubit dynamics. The ion is then returned to the central zone B to perform state readout, which measures the qubit in the computational basis (for more details see Methods). The additional Hamiltonian is implemented by offsetting the laser frequency used in the experiment by a detuning δL. For each setting of toff and δL the experiment is repeated 100 times, allowing us to obtain an estimate for the qubit populations .


Estimation of a general time-dependent Hamiltonian for a single qubit.

de Clercq LE, Oswald R, Flühmann C, Keitch B, Kienzler D, Lo HY, Marinelli M, Nadlinger D, Negnevitsky V, Home JP - Nat Commun (2016)

Experimental sequence and timing.(a) The experiment is carried out in three zones of the trap indicated by A, B and C. (b) The experimental sequence involves steps (i) through (v). Preparation and readout are carried out on the static ion in zone B. The qubit evolves while the ion is transported through the laser beam in zone B in a transport operation taking the ion from zone A to zone C. (c) Experimental sequence showing the timing of applied laser beams and ion transport, including shutting off the laser beam during transport.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4834628&req=5

f1: Experimental sequence and timing.(a) The experiment is carried out in three zones of the trap indicated by A, B and C. (b) The experimental sequence involves steps (i) through (v). Preparation and readout are carried out on the static ion in zone B. The qubit evolves while the ion is transported through the laser beam in zone B in a transport operation taking the ion from zone A to zone C. (c) Experimental sequence showing the timing of applied laser beams and ion transport, including shutting off the laser beam during transport.
Mentions: The experimental sequence is depicted in Fig. 1. We start in zone B by cooling all motional modes of the ion to using a combination of Doppler and electromagnetically induced transparency cooling23, and then initialize the internal state by optical pumping into . The ion is then transported to zone A, and the laser beam used to implement the Hamiltonian is turned on in zone B. The ion is then transported through this laser beam to zone C. During the passage through the laser beam, we rapidly turn the beam off at time toff and thus stop the qubit dynamics. The ion is then returned to the central zone B to perform state readout, which measures the qubit in the computational basis (for more details see Methods). The additional Hamiltonian is implemented by offsetting the laser frequency used in the experiment by a detuning δL. For each setting of toff and δL the experiment is repeated 100 times, allowing us to obtain an estimate for the qubit populations .

Bottom Line: The initially unknown Hamiltonian arises from transporting an ion through a static laser beam.Hamiltonian estimation allows us to estimate the spatial beam intensity profile and the ion velocity as a function of time.The estimation technique is general enough that it can be applied to other quantum systems, aiding the pursuit of high-operational fidelities in quantum control.

View Article: PubMed Central - PubMed

Affiliation: Institute for Quantum Electronics, ETH Zürich, Otto-Stern-Weg 1, 8093 Zürich, Switzerland.

ABSTRACT
The Hamiltonian of a closed quantum system governs its complete time evolution. While Hamiltonians with time-variation in a single basis can be recovered using a variety of methods, for more general Hamiltonians the presence of non-commuting terms complicates the reconstruction. Here using a single trapped ion, we propose and experimentally demonstrate a method for estimating a time-dependent Hamiltonian of a single qubit. We measure the time evolution of the qubit in a fixed basis as a function of a time-independent offset term added to the Hamiltonian. The initially unknown Hamiltonian arises from transporting an ion through a static laser beam. Hamiltonian estimation allows us to estimate the spatial beam intensity profile and the ion velocity as a function of time. The estimation technique is general enough that it can be applied to other quantum systems, aiding the pursuit of high-operational fidelities in quantum control.

No MeSH data available.


Related in: MedlinePlus