We have observed a few distinct anomalous avoided level crossings and voltage-dependent transitions in the excited-state spectrum of an $\text{Al}/{\text{AlO}}_{x}/\text{Al}$ Cooper-pair box (CPB). The device was measured at 40 mK in the 15--50 GHz frequency range. We find that a given level crosses the CPB spectrum at two different gate voltages; the frequency and splitting size of the two crossings differ and the splitting size depends on the Josephson energy of the CPB. We show that this behavior is not only consistent with the CPB being coupled to discrete charged ``two-level'' quantum systems, which move atomic distances in the CPB junctions, but that the spectra provide information about the fluctuators, which is not available from phase qubit spectra of anomalous avoided levels. In particular by fitting a model Hamiltonian to our data, we extract microscopic parameters for each fluctuator, including well asymmetry, tunneling amplitude, and the minimum hopping distance for each fluctuator. The tunneling rates range from less than 3.5--13 GHz, which represent values between 5 and 150% of the well asymmetry, and the dipole moments give a minimum hopping distance of $0.3--0.8\text{ }\text{\AA{}}$ . We have also found that these discrete two-level systems have a pronounced effect on the relaxation time $({T}_{1})$ of the quantum states of the CPB and hence can be a source of dissipation for superconducting quantum bits.We have observed a few distinct anomalous avoided level crossings and voltage-dependent transitions in the excited-state spectrum of an $\text{Al}/{\text{AlO}}_{x}/\text{Al}$ Cooper-pair box (CPB). The device was measured at 40 mK in the 15--50 GHz frequency range. We find that a given level crosses the CPB spectrum at two different gate voltages; the frequency and splitting size of the two crossings differ and the splitting size depends on the Josephson energy of the CPB. We show that this behavior is not only consistent with the CPB being coupled to discrete charged ``two-level'' quantum systems, which move atomic distances in the CPB junctions, but that the spectra provide information about the fluctuators, which is not available from phase qubit spectra of anomalous avoided levels. In particular by fitting a model Hamiltonian to our data, we extract microscopic parameters for each fluctuator, including well asymmetry, tunneling amplitude, and the minimum hopping distance for each fluctuator. The tunneling rates range from less than 3.5--13 GHz, which represent values between 5 and 150% of the well asymmetry, and the dipole moments give a minimum hopping distance of $0.3--0.8\text{ }\text{\AA{}}$. We have also found that these discrete two-level systems have a pronounced effect on the relaxation time $({T}_{1})$ of the quantum states of the CPB and hence can be a source of dissipation for superconducting quantum bits.

arXiv:0810.2455Physical Review BOct 10, 200847 citations

QUANTUM-STATE MANIPULATIONS IN A COOPER-PAIR BOX

Yasunobu Nakamura, Tsuyoshi Yamamoto, Jaw-Shen Tsai +1 more

Foundations of Quantum Mechanics in the Light of New TechnologyOct 1, 20020 citations

Quantum-State Interference in a Cooper-Pair Box

Yasunobu Nakamura, Yu. A. Pashkin, Jaw-Shen Tsai

Springer eBooksJan 1, 20013 citations

Coherent control of macroscopic quantum states in a single-Cooper-pair box

Yasunobu Nakamura, Yu. A. Pashkin, J. S. Tsai

Abstract A nanometre-scale superconducting electrode connected to a reservoir via a Josephson junction constitutes an artificial two-level electronic system: a single-Cooper-pair box. The two levels consist of charge states (differing by 2e, where e is the electronic charge) that are coupled by tunnelling of Cooper pairs through the junction. Although the two-level system is macroscopic, containing a large number of electrons, the two charge states can be coherently superposed1, 2, 3, 4. The Cooper-pair box has therefore been suggested5, 6, 7 as a candidate for a quantum bit or ‘qubit’—the basic component of a quantum computer. Here we report the observation of quantum oscillations in a single-Cooper-pair box. By applying a short voltage pulse via a gate electrode, we can control the coherent quantum state evolution: the pulse modifies the energies of the two charge states non-adiabatically, bringing them into resonance. The resulting state—a superposition of the two charge states—is detected by a tunnelling current through a probe junction. Our results demonstrate electrical coherent control of a qubit in a solid-state electronic device.Abstract A nanometre-scale superconducting electrode connected to a reservoir via a Josephson junction constitutes an artificial two-level electronic system: a single-Cooper-pair box. The two levels consist of charge states (differing by 2e, where e is the electronic charge) that are coupled by tunnelling of Cooper pairs through the junction. Although the two-level system is macroscopic, containing a large number of electrons, the two charge states can be coherently superposed1, 2, 3, 4. The Cooper-pair box has therefore been suggested5, 6, 7 as a candidate for a quantum bit or ‘qubit’—the basic component of a quantum computer. Here we report the observation of quantum oscillations in a single-Cooper-pair box. By applying a short voltage pulse via a gate electrode, we can control the coherent quantum state evolution: the pulse modifies the energies of the two charge states non-adiabatically, bringing them into resonance. The resulting state—a superposition of the two charge states—is detected by a tunnelling current through a probe junction. Our results demonstrate electrical coherent control of a qubit in a solid-state electronic device.

Apr 29, 19991,507 citations

Spectroscopy of a Cooper-pair box coupled to a two-level system via charge and critical current

V. Zaretskey, Baladitya Suri, S P Novikov +2 more

We report on the quadrupling of the transition spectrum of an Al/AlO ${}_{x}$ /Al Cooper-pair box (CPB) charge qubit in the $4.0--7.3$ GHz frequency range. The qubit was coupled to a quasilumped-element Al superconducting resonator and measured at a temperature of 25 mK. We obtained good matches between the observed spectrum and the spectra calculated from a model Hamiltonian containing two distinct low-excitation energy two-level systems (TLS) coupled to the CPB. In our model, each TLS has a charge that tunnels between two sites in a local potential and induces a change in the CPB critical current. By fitting the model to the spectrum, we have extracted microscopic parameters of the fluctuators including the well asymmetry, tunneling rate, and a surprisingly large fractional change ( $30%--40%$ ) in the critical current (12 nA). This large change is consistent with a Josephson junction with a nonuniform tunnel barrier containing a few dominant conduction channels and a TLS that modulates one of them.We report on the quadrupling of the transition spectrum of an Al/AlO${}_{x}$/Al Cooper-pair box (CPB) charge qubit in the $4.0--7.3$ GHz frequency range. The qubit was coupled to a quasilumped-element Al superconducting resonator and measured at a temperature of 25 mK. We obtained good matches between the observed spectrum and the spectra calculated from a model Hamiltonian containing two distinct low-excitation energy two-level systems (TLS) coupled to the CPB. In our model, each TLS has a charge that tunnels between two sites in a local potential and induces a change in the CPB critical current. By fitting the model to the spectrum, we have extracted microscopic parameters of the fluctuators including the well asymmetry, tunneling rate, and a surprisingly large fractional change ($30%--40%$) in the critical current (12 nA). This large change is consistent with a Josephson junction with a nonuniform tunnel barrier containing a few dominant conduction channels and a TLS that modulates one of them.

arXiv:1305.3962Physical Review BMay 28, 201318 citations

Coherent Manipulations of Charge-Number States in a Cooper-Pair Box

Yasunobu Nakamura, Yu. A. Pashkin, Tsuyoshi Yamamoto +1 more

Condensation and Coherence in Condensed MatterMar 1, 20030 citations

We have observed a few distinct anomalous avoided level crossings and voltage-dependent transitions in the excited-state spectrum of an

\text{Al}/{\text{AlO}}_{x}/\text{Al}

Cooper-pair box (CPB). The device was measured at 40 mK in the 15--50 GHz frequency range. We find that a given level crosses the CPB spectrum at two different gate voltages; the frequency and splitting size of the two crossings differ and the splitting size depends on the Josephson energy of the CPB. We show that this behavior is not only consistent with the CPB being coupled to discrete charged ``two-level'' quantum systems, which move atomic distances in the CPB junctions, but that the spectra provide information about the fluctuators, which is not available from phase qubit spectra of anomalous avoided levels. In particular by fitting a model Hamiltonian to our data, we extract microscopic parameters for each fluctuator, including well asymmetry, tunneling amplitude, and the minimum hopping distance for each fluctuator. The tunneling rates range from less than 3.5--13 GHz, which represent values between 5 and 150% of the well asymmetry, and the dipole moments give a minimum hopping distance of

0.3--0.8\text{ }\text{\AA{}}

. We have also found that these discrete two-level systems have a pronounced effect on the relaxation time

({T}_{1})

of the quantum states of the CPB and hence can be a source of dissipation for superconducting quantum bits.

We report on the quadrupling of the transition spectrum of an Al/AlO

{}_{x}

/Al Cooper-pair box (CPB) charge qubit in the

4.0--7.3

GHz frequency range. The qubit was coupled to a quasilumped-element Al superconducting resonator and measured at a temperature of 25 mK. We obtained good matches between the observed spectrum and the spectra calculated from a model Hamiltonian containing two distinct low-excitation energy two-level systems (TLS) coupled to the CPB. In our model, each TLS has a charge that tunnels between two sites in a local potential and induces a change in the CPB critical current. By fitting the model to the spectrum, we have extracted microscopic parameters of the fluctuators including the well asymmetry, tunneling rate, and a surprisingly large fractional change (

30%--40%

) in the critical current (12 nA). This large change is consistent with a Josephson junction with a nonuniform tunnel barrier containing a few dominant conduction channels and a TLS that modulates one of them.