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Physical Review A

Characterization of coherent population-trapped states in a circuit-QED Λ system

Shavindra Premaratne, F. C. Wellstood, B. S. Palmer

Published Oct 25, 2017• 4 citations
Publisher

Abstract

We examine coherent population trapping in a circuit-QED system consisting of an Al/${\mathrm{AlO}}_{x}$/Al transmon qubit embedded in an Al three-dimensional cavity. By engineering the dissipation rate of the cavity to be much larger than that of the qubit and continuously pumping a two-photon process to an excited state of the cavity-qubit system, we are able to invert the population into the qubit excited state with a fidelity of 94%. Applying a second continuous drive tone at the dressed cavity frequency forms an effective $\mathrm{\ensuremath{\Lambda}}$ system and enables us to coherently trap the system in a dark state formed from a superposition of the excited and ground states of the qubit. By performing quantum state tomography we demonstrate that the position of the dark state on the Bloch sphere can be controlled by changing the relative amplitudes and phases of the two drives.

DOI
10.1103/physreva.96.043858

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We examine coherent population trapping in a circuit-QED system consisting of an Al/AlOx{\mathrm{AlO}}_{x}AlOx​/Al transmon qubit embedded in an Al three-dimensional cavity. By engineering the dissipation rate of the cavity to be much larger than that of the qubit and continuously pumping a two-photon process to an excited state of the cavity-qubit system, we are able to invert the population into the qubit excited state with a fidelity of 94%. Applying a second continuous drive tone at the dressed cavity frequency forms an effective \ensuremathΛ\mathrm{\ensuremath{\Lambda}}\ensuremathΛ system and enables us to coherently trap the system in a dark state formed from a superposition of the excited and ground states of the qubit. By performing quantum state tomography we demonstrate that the position of the dark state on the Bloch sphere can be controlled by changing the relative amplitudes and phases of the two drives.
We show that an arbitrary system described by two dipole moments exhibits coherent superpositions of internal states that can be completely decoupled from the dissipative interactions (responsible for decoherence) and an external driving laser field. These superpositions, known as dark or trapping states, can be completely stable or can coherently interact with the remaining states. We examine the master equation describing the dissipative evolution of the system and identify conditions for population trapping and also classify processes that can transfer the population to these undriven and nondecaying states. It is shown that coherent transfers are possible only if the two systems are nonidentical, that is the transitions have different frequencies and/or decay rates. In particular, we find that the trapping conditions can involve both coherent and dissipative interactions, and depending on the energy level structure of the system, the population can be trapped in a linear superposition of two or more bare states, a dressed state corresponding to an eigenstate of the system plus external fields or, in some cases, in one of the excited states of the system. A comprehensive analysis is presented of the different processes that are responsible for population trapping, and we illustrate these ideas with three examples of two coupled systems: single V- and $\ensuremath{\Lambda}$-type three-level atoms and two nonidentical two-level atoms, which are known to exhibit dark states. We show that the effect of population trapping does not necessarily require decoupling of the antisymmetric superposition from the dissipative interactions. We also find that the vacuum-induced coherent coupling between the systems could be easily observed in $\ensuremath{\Lambda}$-type atoms. Our analysis of the population trapping in two nonidentical atoms shows that the atoms can be driven into a maximally entangled state which is completely decoupled from the dissipative interaction.
Spin squeezing has important applications in the field of quantum metrology and quantum information processing. Here we propose that coherent population trapping is well suitable for establishing cavity dissipation mechanism and generating a spin-squeezed state. An ensemble of N double Λ -type atoms is placed inside the two-mode optical cavity, where one Λ subsystem is driven resonantly by two strong control fields to form a dark resonance and the other Λ subsystem is coupled by two cavity vacuum fields and two external fields with large detunings. Due to the dark resonance, the atoms are trapped in a dark state and one has the maximal coherence between the two ground states. Two double off-resonance stimulated Raman scattering interactions are induced between fields and dressed atoms to establish a dissipative quantum dynamical process based on a collective cavity reservoir. As a result, strong stable spin squeezing is generated, which is verified by our numerical and analytical results. Published by the American Physical Society 2024
The stimulated Raman adiabatic passage (STIRAP) allows selective, coherent population transfer in a three-level quantum system by the adiabatic control of two suitably chosen envelopes and delayed laser pulses. However, the long operation time involved with the adiabatic protocols makes them more susceptible to decay and decoherence. A shortcut-to-adiabaticity technique, namely, counterdiabatic driving (CD), suppresses the decoherence-induced loss by speeding up the STIRAP process, thereby enhancing the efficiency and fidelity of population transfer. The superadiabatic STIRAP (saSTIRAP) method requires the application of a shortcut drive or CD pulse, which couples the coherently trapped states in a three-level quantum system. Hence, the closed-loop $\mathrm{\ensuremath{\Lambda}}$ system consisting of all electric dipole-allowed transitions is an essential requirement for saSTIRAP, which is rarely admissible in a natural atom. This paper theoretically investigates an experimentally feasible model for implementing saSTIRAP using a closed-loop $\mathrm{\ensuremath{\Lambda}}$ system with doubly dressed polariton states in a driven circuit QED system. We show a population transfer with efficiencies close to 80.7580.75%80.75 and 98.1098.10%98.10 with fidelities of 89.8689.86%89.86 and 99.0499.04%99.04 for the resonant STIRAP and saSTIRAP protocols, respectively, with experimentally feasible parameters. The efficiency of the population transfer can be further increased by improving the coherence times of the cavity and the transmon qubit. This work may be useful in designing fast, efficient quantum gates for applications in quantum technologies.
We report our study on coherent population trapping (CPT) in a $\ensuremath{\Lambda}$ configuration coupled by magnetic dipole interactions. The $\ensuremath{\Lambda}$ configuration is formed by bichromatic radio-frequency fields coupling a pair of Zeeman sublevels in one hyperfine level of an alkali-metal atom to another sublevel in the other hyperfine level. The Zeeman sublevel at the apex is coupled to a state in the nPnPnP manifold via an optical transition on one of the spectroscopic DDD lines to induce optical pumping to a dark state. The configuration is closed without leakage to other Zeeman sublevels. We use lithium atoms in an optical trap for our experimental study. The system allows independent control of the main parameters characterizing CPT, which include the upper-state decay rate and the decoherence rate as well as the Rabi frequencies. By turning off the applied fields, the system is frozen so that its quantum state can be measured precisely. We studied the line shapes and dynamics of the CPT system, and measured the phase relation of the dark superposition state to find excellent agreement with theory. The possible application of the scheme as a method to cool optically trapped atoms below the recoil limit in a manner analogous to velocity-selective coherent population trapping is discussed.
In the circuit quantum electrodynamics architecture, both the resonance frequency and the coupling of superconducting qubits to microwave field modes can be controlled via external electric and magnetic fields to explore qubit-photon dynamics in a wide parameter range. Here, we experimentally demonstrate and analyze a scheme for tuning the coupling between a transmon qubit and a microwave resonator using a single coherent drive tone. We treat the transmon as a three-level system, with the qubit subspace defined by the ground and the second excited states. If the drive frequency matches the difference between the resonator and the qubit frequencies, a Jaynes-Cummings-type interaction is induced, which is tunable in both amplitude and phase. We show that coupling strengths of about 10 MHz can be achieved in our setup, limited only by the anharmonicity of the transmon qubit. This scheme has been successfully used to generate microwave photons with a controlled temporal shape [M. Pechal et al., Phys. Rev. X 4, 041010 (2014)] and can be directly implemented with superconducting quantum devices featuring larger anharmonicity for higher coupling strengths.
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 multilevel 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 a phase qubit. We observe 60(+/-7)% suppression of the excited state population under conditions of CPT resonance. We present data and matching theoretical simulations showing the development of CPT in time. Finally, we used the observed time dependence of the excited state population to characterize quantum dephasing times of the system.