A number of superconducting qubits, such as the transmon or the phase qubit, have an energy level structure with small anharmonicity. This allows for convenient access of higher excited states with similar frequencies. However, special care has to be taken to avoid unwanted higher-level populations when using short control pulses. Here we demonstrate the preparation of arbitrary three level superposition states using optimal control techniques in a transmon. Performing dispersive readout, we extract the populations of all three levels of the qutrit and study the coherence of its excited states. Finally we demonstrate full quantum state tomography of the prepared qutrit states and evaluate the fidelities of a set of states, finding on average 95%.A number of superconducting qubits, such as the transmon or the phase qubit, have an energy level structure with small anharmonicity. This allows for convenient access of higher excited states with similar frequencies. However, special care has to be taken to avoid unwanted higher-level populations when using short control pulses. Here we demonstrate the preparation of arbitrary three level superposition states using optimal control techniques in a transmon. Performing dispersive readout, we extract the populations of all three levels of the qutrit and study the coherence of its excited states. Finally we demonstrate full quantum state tomography of the prepared qutrit states and evaluate the fidelities of a set of states, finding on average 95%.

arXiv:1004.5504Physical Review LettersNov 24, 2010164 citations

Quantum control of atoms and molecules

de Araújo, E Luis Eduardo

Jun 1, 20011 citation

Tomography, control, and characterization of entanglement in a three-level atomic system

S. N. Sandhya, V. Ravishankar

We study the quantum correlations of the radiation emitted by three-level atoms (cascade type) interacting with two driving fields. In the linear regime, and in the Weisskopf-Wigner approximation, we show that the atomic and the two-photon density matrix are equivalent to each other. This facilitates the tomography of the two-mode state to be realized by measurements on either the atomic system or the emitted fields. While, in general, one needs ${4}^{N}$ measurements for the tomography of an $N$ -photon state, we show that one needs $(N+1){}^{2}\ensuremath{-}1$ observables for the tomography of photons emitted by an atomic system. Thus there is an exponential reduction in the number of observables for the reconstruction of the class of $N$ -photon states emitted by atoms. We show that the driving field strengths and detunings provide the control parameters for the preparation of a specific target state. Finally, we study the characterization of entanglement of the two-photon state. We observe that a characterization of entanglement in terms of a single parameter is not possible when the system is in a mixed state; therefore, we provide a description in terms of the newly introduced probability distribution for entanglement, in various regimes of interest.We study the quantum correlations of the radiation emitted by three-level atoms (cascade type) interacting with two driving fields. In the linear regime, and in the Weisskopf-Wigner approximation, we show that the atomic and the two-photon density matrix are equivalent to each other. This facilitates the tomography of the two-mode state to be realized by measurements on either the atomic system or the emitted fields. While, in general, one needs ${4}^{N}$ measurements for the tomography of an $N$-photon state, we show that one needs $(N+1){}^{2}\ensuremath{-}1$ observables for the tomography of photons emitted by an atomic system. Thus there is an exponential reduction in the number of observables for the reconstruction of the class of $N$-photon states emitted by atoms. We show that the driving field strengths and detunings provide the control parameters for the preparation of a specific target state. Finally, we study the characterization of entanglement of the two-photon state. We observe that a characterization of entanglement in terms of a single parameter is not possible when the system is in a mixed state; therefore, we provide a description in terms of the newly introduced probability distribution for entanglement, in various regimes of interest.

arXiv:1004.4739Physical Review ADec 2, 20108 citations

Quantum Tomography

Giacomo Mauro D’Ariano, Matteo G. A. Paris, Massimiliano Federico Sacchi

arXiv:quant-ph/0302028Advances in imaging and electron physicsJan 1, 2003227 citations

{4}^{N}

measurements for the tomography of an

N

-photon state, we show that one needs $(N+1){}^{2}\ensuremath{-}1$ observables for the tomography of photons emitted by an atomic system. Thus there is an exponential reduction in the number of observables for the reconstruction of the class of

N

-photon states emitted by atoms. We show that the driving field strengths and detunings provide the control parameters for the preparation of a specific target state. Finally, we study the characterization of entanglement of the two-photon state. We observe that a characterization of entanglement in terms of a single parameter is not possible when the system is in a mixed state; therefore, we provide a description in terms of the newly introduced probability distribution for entanglement, in various regimes of interest.