Electromagnetically induced transparency in a superconducting three-level system (original) (raw)
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Autler-Townes Effect in a Superconducting Three-Level System
Physical Review Letters, 2009
When a three-level quantum system is irradiated by an intense coupling field resonant with two of the three possible transitions, the resonant absorption of the system from its ground state by an additional radiation field is suppressed. This effect, where the population is trapped in the ground state, is known in quantum optics as "electromagnetically induced transparency". When the coupling field is detuned from resonance, the resonant absorption peak splits to form an "Autler-Townes doublet". We observe these phenomena in a superconducting Josephson phase qubit, which can be considered an "artificial atom" with a multilevel quantum structure. These observations are qualitatively described by a simple model restricted to three energy levels. A full solution of the master equation including higher levels provides excellent agreement with all the experimental data.
2010
We study the microwave absorption of a driven three-level quantum system, which is realized by a superconducting flux quantum circuit (SFQC), with a magnetic driving field applied to the two upper levels. The interaction between the three-level system and its environment is studied within the Born-Markov approximation, and we take into account the effects of the driving field on the damping rates of the three-level system. We study the linear response of the driven three-level SFQC to a weak probe field. The linear magnetic susceptibility of the SFQC can be changed by both the driving field and the bias magnetic flux. When the bias magnetic flux is at the optimal point, the transition from the ground state to the second excited state is forbidden and the three-level SFQC has a ladder-type transition. Thus, the SFQC responds to the probe field like natural atoms with ladder-type transitions. However, when the bias magnetic flux deviates from the optimal point, the three-level SFQC has a cyclic transition, thus it responds to the probe field like a combination of natural atoms with ladder-type transitions and natural atoms with Λ-type transitions. In particular, we provide detailed discussions on the conditions for realizing electromagnetically induced transparency and Autler-Townes splitting in three-level SFQCs.
Tunable electromagnetically induced transparency and absorption with dressed superconducting qubits
Physical Review a, 2010
Electromagnetically induced transparency and absorption (EIT and EIA) are usually demonstrated using three-level atomic systems. In contrast to the usual case, we theoretically study the EIT and EIA in an equivalent three-level system: a superconducting two-level system (qubit) dressed by a single-mode cavity field. In this equivalent system, we find that both the EIT and the EIA can be tuned by controlling the level-spacing of the superconducting qubit and hence controlling the dressed system. This tunability is due to the dressed relaxation and dephasing rates which vary parametrically with the level-spacing of the original qubit and thus affect the transition properties of the dressed qubit and the susceptibility. These dressed relaxation and dephasing rates characterize the reaction of the dressed qubit to an incident probe field. Using recent experimental data on superconducting qubits (charge, phase, and flux qubits) to demonstrate our approach, we show the possibility of experimentally realizing this proposal.
Physical Review B, 2011
We present a detailed theoretical analysis of a multi-level quantum system coupled to two radiation fields and subject to decoherence. We concentrate on an effect known from quantum optics as the Autler-Townes splitting, which has been recently demonstrated experimentally [M. A. Sillanpää et al., Phys. Rev. Lett. 103, 193601 (2009)] in a superconducting phase qubit. In the three-level approximation, we derive analytical solutions and describe how they can be used to extract the decoherence rates and to account for the measurement data. Better agreement with the experiment can be obtained by extending this model to five levels. Finally, we investigate the stationary states created in the experiment and show that their structure is close to that of dark states.
Electromagnetically Induced Transparency in a Double Well Atomic Josephson Junction
Acta Physica Polonica Series a, 2009
Electromagnetically induced transparency is an important tool for controlling light propagation and nonlinear wave mixing in atomic gases with potential applications ranging from quantum computing to table top tests of general relativity. Here we consider electromagnetically induced transparency in an atomic Bose-Einstein condensate trapped in a double well potential. One well is prepared as in standard electromagnetically induced transparency with a weak probe laser and control laser in a Λ configuration while tunneling between the wells provides a coherent coupling between identical electronic states in the two wells leading to the formation of spatially delocalized inter-well dressed states. The macroscopic inter-well coherence of the Bose-Einstein condensate wave function qualitatively modifies the normal electromagnetically induced transparency linear susceptibility and leads to the formation of additional absorption resonances and larger dispersion than electromagnetically induced transparency. We show that these new resonances can be interpreted in terms of the inter-well dressed states and the formation of a novel type of dark state involving the control laser and the inter-well tunneling.
Electromagnetically induced transparency and coherent-state preparation in optically thick media
We study the microwave absorption of a driven three-level quantum system, which is realized by a superconducting flux quantum circuit (SFQC), with a magnetic driving field applied to the two upper levels. The interaction between the three-level system and its environment is studied within the Born-Markov approximation, and we take into account the effects of the driving field on the damping rates of the three-level system. We study the linear response of the driven three-level SFQC to a weak probe field. The linear magnetic susceptibility of the SFQC can be changed by both the driving field and the bias magnetic flux. When the bias magnetic flux is at the optimal point, the transition from the ground state to the second excited state is forbidden and the three-level SFQC has a ladder-type transition. Thus, the SFQC responds to the probe field like natural atoms with ladder-type transitions. However, when the bias magnetic flux deviates from the optimal point, the three-level SFQC has a cyclic transition, thus it responds to the probe field like a combination of natural atoms with ladder-type transitions and natural atoms with Λ-type transitions. In particular, we provide detailed discussions on the conditions for realizing electromagnetically induced transparency and Autler-Townes splitting in three-level SFQCs.
Measurement of Autler-Townes and Mollow Transitions in a Strongly Driven Superconducting Qubit
Physical Review Letters, 2009
We present spectroscopic measurements of the Autler-Townes doublet and the sidebands of the Mollow triplet in a driven superconducting qubit. The ground to first excited state transition of the qubit is strongly pumped while the resulting dressed qubit spectrum is probed with a weak tone. The corresponding transitions are detected using dispersive read-out of the qubit coupled off-resonantly to a microwave transmission line resonator. The observed frequencies of the Autler-Townes and Mollow spectral lines are in good agreement with a dispersive Jaynes-Cummings model taking into account higher excited qubit states and dispersive level shifts due to off-resonant drives.
Electromagnetically Induced Transparency with Amplification in Superconducting Circuits
Physical Review Letters, 2010
We show that controlling relative phases of electromagnetic fields driving an atom with a Delta-configuration energy-level structure enables optical susceptibility to be engineered in novel ways. In particular, relative-phase control can yield electromagnetically induced transparency but with the benefit that the transparency window is sandwiched between an absorption and an amplification band rather than between two absorption bands in typical
Control and Tomography of a Three Level Superconducting Artificial Atom
Physical Review Letters, 2010
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 96%. PACS numbers: 42.50.Ct, 42.50.Pq, 78.20.Bh, 85.25.Am Spin 1/2 or equivalent two-level systems are the most common computational primitive for quantum information processing . Using physical systems with higher dimensional Hilbert spaces instead of qubits has a number of potential advantages. They simplify quantum gates [2], can naturally simulate physical systems with spin greater than 1/2 [3], improve security in quantum key distribution and show stronger violations of local realism when prepared in entangled states . Multilevel systems have been successfully realized in photon orbital angular momentum states , energy-time entangled qutrits [10] and polarization states of multiple photons . Multiple levels were used before for pumpprobe readout of superconducting phase qubits , were observed in the nonlinear scaling of the Rabi frequency of DC SQUID's and were explicitly populated and used to emulate the dynamics of single spins . In solid state devices, the experimental demonstration of full quantum state tomography [10] of the generated states, i.e. a full characterization of the qutrit, is currently actively pursued by a number of groups.