Session Z26: Superconducting Qubits: New States and Effects

Quantum Interference Induced by Landau-Zener Transition in Strongly Driven Flux Qubits

We irradiate superconducting flux qubits with strong microwaves. Quantum interference patterns corresponding to the population transitions between discrete macroscopic quantum states were observed. The interference patterns, which depend on the microwave frequency and power, are complicated because of the short decoherence time. An analytical model based on Landau-Zener transition is developed to quantitatively describe the interference patterns. This work is partially supported by NSFC (10704034, 10725415), the State Key Program for Basic Research of China (2006CB921801).   

Coherent Population Trapping in a Superconducting Phase Qubit

The phenomenon of Coherent Population Trapping (CPT) of an atom (or solid state ``artificial atom''), and the associated effect of Electromagnetically Induced Transparency (EIT), are clear demonstrations of quantum interference due to coherence in multi-level quantum systems. We report observation of CPT in a superconducting phase qubit by simultaneously driving two coherent transitions in a $\Lambda$-type configuration, utilizing the three lowest lying levels of a local minimum of the phase qubit. We observe $\sim 60$\% suppression of excited state population under conditions of two-photon resonance, where EIT and CPT are expected to occur. We present data and matching theoretical simulations showing the development of CPT in time. We also used the observed time dependence of the excited state population to characterize quantum dephasing times of the system, as predicted in [1]. [1] K.V. Murali, Z. Dutton, W.D. Oliver, D.S. Crankshaw, and T.P.Orlando, Phys. Rev. Lett. {\bf 93}, 087003 (2004).   

Generation of three-qubit entangled states using superconducting phase qubits

Entanglement is one of the crucial resources necessary for quantum computation. For three qubits, there are two fundamentally different types of entanglement, typified by the states $\left|\mathrm{GHZ}\right\rangle = \left|000\right\rangle + \left|111\right\rangle$ and $\left|\mathrm{W}\right\rangle = \left|100\right\rangle + \left|010\right\rangle + \left|001\right\rangle$. Using three capacitively-coupled phase qubits, we have implemented protocols designed for fast single-step generation of these states. The resulting states were characterized with quantum state tomography and compared with entanglement witnesses that identify true multi-partite entanglement.   

Bistability of qubit chains coupled to a superconducting resonator

When a quantum many-body system is coupled to a cavity, the cavity not only can be used to probe the quantum phase transition but can also induce novel effects in the many-body system. In this work, we study the bistable effect in a chain of superconducting qubits coupled to a superconducting resonator cavity. The qubits are connected to their nearest neighbors capacitively and form a transverse Ising model. Using a semiclassical approach to treat the resonator in the bad cavity limit, we show that a bistable regime exists where the ground state of the transverse Ising model can be in either the paramagnetic state or the ferromagnetic state as the driving of the resonator increases. In a full quantum calculation including the resonator damping and the qubit decoherence, the photon distribution of the resonator shows bimodular behavior which agrees well the bistable solutions in the semiclassical approach.   

Autler-Townes effect in a superconducting three-level system

When a three-level quantum system is irradiated by an intense coupling field resonant with one of the three possible transitions, the absorption peak of an additional probe field involving the remaining level is split. This process is known in quantum optics as the Autler-Townes effect. We observe these phenomena in a superconducting Josephson phase qubit, which can be considered an ``artificial atom'' with a multilevel quantum structure. The spectroscopy peaks can be explained reasonably well by a simple three-level Hamiltonian model. Simulation of a more complete model (including dissipation, higher levels, and cross-coupling) provides excellent agreement with all the experimental data.   

Landau-Zener-Stueckelberg interferometry with low- and high-frequency driving

The problem of a periodically driven two-level system cannot be solved exactly. The rotating-wave approximation (RWA) is the most common approximation used to analyze this problem. I will discuss an alternative approximation that applies in the case of very strong driving, where the RWA is generally invalid. The dynamics is approximated by a sequence of Landau-Zener transitions that can interfere constructively or destructively, depending on the Stueckelberg phase accumulated between transitions. It turns out that the resonance conditions are qualitatively different for the cases of low- and high-frequency driving. I will discuss the two respective limits. I will also show that our theoretical results describe recent experiments on Landau-Zener-Stuckelberg interferometry with superconducting qubits [S.N. Shevchenko, S. Ashhab, and F. Nori, arXiv:0911.1917].   

The size of superposition states in flux qubits

Flux qubits, small superconducting loops interrupted by Josephson junctions, are successful realizations of quantum coherence for macroscopic variables. Superconductivity in these loops is carried by $\sim 10^6$ -- $10^{10}$ electrons, which has been interpreted as suggesting that coherent superpositions of such current states are macroscopic superpositions as exemplified in the extreme case by Schr\"odinger's 1935 gedanken experiment. We provide a full microscopic analysis of such qubits, from which the macroscopic quantum description can be derived. This reveals that the number of microscopic constituents participating in superposition states for experimentally accessible flux qubits is surprisingly but not trivially small. The combination of this relatively small size with large differences between macroscopic observables in the two branches is seen to result from the Fermi statistics of the electrons and from the large disparity between the values of superfluid and Fermi velocity in these systems.   

Time-domain observation of macroscopic quantum coherence

Thirty years ago, A. J. Leggett proposed that a superconducting loop interrupted by a Josephson tunnel junction might display a coherent oscillation between trapping and detrapping of a single flux quantum. This phenomenon of reversible quantum tunneling between two classically separable states of identical energy, known as Macroscopic Quantum Coherence (MQC), is regarded crucial for precise tests of whether macroscopic systems such as circuits fully obey quantum mechanics. We report time-domain observation of MQC oscillations at sub-GHz frequency and quality factor larger than 500. Two major innovations have been introduced to achieve this result: (i) the loop inductance is 10,000 larger than in previous experiments, allowing the junction to enter the charging regime and (ii) a novel microwave cavity-assisted readout scheme free of Purcell effect. Contrary to expectations, we find that the MQC transition could be the basis of a superconducting qubit of improved coherence and readout fidelity.   

Electromagnetically-induced transparency combined with lasing without inversion in superconducting qubits

By strongly driving a transition of a three-level atom one dresses the atomic states with the external field resulting in an Autler-Townes energy level splitting. The absorption and dispersion properties of the medium can then be controlled optically in order to realize effects such as electromagnetically-induced transparency (EIT) and lasing without inversion (LWI). In atomic systems, these two effects are however usually not realized together. Away from their symmetry point, both the flux qubit and the fluxonium form a $\Delta$-configuration where transitions between any two of the lowest three states are allowed. When driven by two resonant fields, we show that the system exhibits a transparency frequency window sandwiched between an absorption band (EIT) on one side and an amplification band (LWI) on the other. Finally, we discuss a possible implementation and measurement scheme using the flux qubit or the fluxonium charge qubit.   

Measurements of Microwave Single Photon Correlations: Theory

Superconducting circuit implementations of cavity QED have enabled the exploration of various regimes of light-matter interaction. In this work, we present theoretical aspects of the observation of quantum properties of the field emitted from a cavity without access to non-linear/single-photon detectors (which have not been demonstrated reliably in the microwave regime). In particular, we focus on how to perform the measurement of optical coherence functions in pulsed circuit QED experiments using field quadrature measurements of the outputs of a two-sided cavity. We illustrate how the standard Hanbury Brown and Twiss setup can be replaced with the monitoring of these cavity outputs, while still allowing for the calculation of arbitrary first and second order correlation functions. Moreover, we illustrate how the significant noise contributions from thermal fields, amplifiers and mixers can be accounted and compensated for.   

Measurements of Microwave Single Photon Correlations: Experiment

Circuit QED allows for excellent control and measurement of the quantum mechanical properties of qubits, photons and their interactions. As a result, circuit QED is an ideal testbed to investigate the quantum nature of light. In our experiments we prepare a complete family of zero and one photon superposition states in a high quality on-chip resonator by controlling single qubit Rabi and qubit-cavity vacuum Rabi oscillations. By detecting the emitted radiation at both outputs of a symetric two-sided cavity, we are able to perform time-resolved measurements of the cavity field quadratures, photon number and the first-order correlation function. We characterize the prepared field states and also show that we are able to cool a small thermal background field present in the cavity to below its thermal equilibrium value. Furthermore we suggest that any correlation which can be expressed in terms of the cavity field operators can be measured by using beam splitters, homodyne detection and efficient real time signal processing.   

State tomography of a three-level superconducting quantum circuit

Coherent control of higher than two-dimensional quantum systems can considerably improve present techniques for quantum information processing. In particular, superconducting quantum circuits can be operated in a regime with closely spaced energy levels, where arbitrary superposition states can be prepared by applying appropriately shaped microwave pulses at different frequencies. We employ dispersive read-out [1] to discriminate the population of upper energy levels of superconducting transmon circuits coupled to a coplanar microwave resonator. This allows us to determine the dynamics in the restricted two-dimensional qubit subspace and assess the population transfer to the third level. Finally, we fully characterize arbitrary three-dimensional qutrit states by a complete tomographic measurement.\\[4pt] [1] R. Bianchetti \emph{et al.}, Phys.~Rev.~A {\bf 80}, 043840 (2009).   

Tomography of a superconducting phase qutrit

Benchmarking the fidelity of quantum state preparation and evolution is vital for further advances in quantum engineering. State and process tomography are normally used for such benchmarking of individual qubit and coupled qubit systems. We extend this procedure to a superconducting phase circuit operating with three levels (qutrit), and measure the 3X3 density matrix for a set of arbitrary prepared states and their evolution. We quantify the diagonal and off diagonal decays due to relaxation and decoherence and compare to simulation.   

Tomographic reconstruction of the Wigner function of an itinerant microwave field

In an increasing number of experiments, dispersive coupling is successfully used to encode the state of nanomechanical resonators or superconducting qubits onto the state of a microwave field. However most the information is lost due to the poor quantum efficiency of the best commercially available microwave amplifiers. To circumvent this limitation our lab has been developing quantum limited Josephson Parametric Amplifiers (JPAs). In this talk we will present an application of the JPA leading to a dramatic increase of the performance of the Quantum State Tomography. It has enabled us to reconstruct the Wigner function of a squeezed state of the microwave field. We will discuss the achieved degree of squeezing and the quantum efficiency of the state tomography, from the perspective of using these squeezed states as building blocks for quantum information experiments. Indeed these states, which are highly non-classical and are easily generated by JPAs, form EPR like states when combined together and thus are the basis of a complete quantum information processing strategy, known as the continuous variables quantum information.   

Rapid Adiabatic Passage for robust quantum gates

Rapid adiabatic passage has been suggested as tool to coherently transfer population between two capacitively coupled phase qubits. Together with single qubit rotations, rapid adiabatic passage can be used to generate universal logic gates for quantum computing. In this talk we will describe our experimental effort to use rapid adiabatic passage to transfer an excitation between two phase qubits capacitively coupled to a coplanar waveguide.