Scientists successfully manipulate 'dark state' to increase qubit storage time by 500 times

In a Nature Physics paper published on March 14 [1], Gerhard Kirchmair's team at the Institute of Quantum Optics and Quantum Information (IQOQI) of the Austrian Academy of Sciences has successfully manipulated the superconducting qubit for the first time by coupling it to a . A quantum state called a "dark state" is created.

Superconducting qubits waveguidecoupled to waveguides have long-range interactions mediated by photons, leading to the emergence of collective states. Destructive interference between qubits decouples the collective dark state from the waveguide environment. Their inability to emit photons into waveguides makes dark states an invaluable resource for preparing long-lived quantum many-body states and implementing quantum information protocols in open quantum systems.

"These are entangled quantum states that are completely decoupled from the outside world, so to speak, they are invisible, which is why they are called dark states," said Max Zanner, first author of the paper.

However, the dark states are also separated from the magnetic field driving the waveguides, making manipulating them a challenge. Until now, it has not been possible to properly control and manipulate these dark states without destroying their invisibility. Now, a team led by Gerhard Kirchmair has developed a system that can manipulate the dark state of superconducting circuits in microwave waveguides from the outside.

They built four superconducting qubits into a microwave waveguide and connected control wires through two lateral inlets. Using microwave radiation through these wires, they can manipulate the dark state. Together, the four superconducting circuits form a powerful qubit that can be stored for about 500 times longer than a single circuit. Multiple dark states exist simultaneously in this qubit, which can be used for quantum simulation and quantum information processing.

Achieving collective dark state qubits

In this work, the team demonstrated coherent control of the collective dark state by controlling the interaction between four superconducting qubits and a local driver.

The decoherence rate of a qubit with ground state |g> and excited state |e> is given by its linewidth. The qubit decoherence ratio Γ=(γ+γnr)/2+γφ is the sum of the radiative decay γ of the waveguide mode, the non-radiative energy loss γnr and the pure dephasing γφ.

When the qubits are coupled to the waveguide, the researchers can extract the linewidth in scattering experiments by measuring the transmission or reflection of the waveguide to obtain the γ and nonradiative decoherence ratios γ'nr=γnr/2+γφ.

As shown in Fig. 1(a), on the left are the natural atoms in the photonic crystal waveguide. On the right is a transmon qubit as an artificial atom coupled to the mode continuum. In the strong coupling limit, the decay γ in the waveguide exceeds the non-radiative loss γ'nr.

The device shown in Figure 1(d) consists of four frequency-tunable transmon qubits that act as artificial atoms. Qubits Q1 and Q2 are on the left, closer to the input of the waveguide. Qubits Q3 and Q4 are located on the right, closer to the output of the waveguide, and the physical spacing between these qubit pairs is dy=(46.0±0.5)mm. The spacing between the two qubits in a pair is dx=1mm, which creates capacitive coupling. The cutoff frequency of the fundamental waveguide mode TE01 is ωc/2π=6.55 GHz, and the polarization of the electric field is parallel to the dipole moment of the transmon, so the qubits can be efficiently coupled to the waveguide.

Depending on the symmetry of the electromagnetic environment, multi-qubit collective states acquire superradiant or subradiative behavior according to their respective symmetries. As shown in Fig. 1(b), the symmetry of the collective state is represented by the arrows representing the in-phase and out-of-phase oscillatory transition dipole moments.

For two qubits separated by d=λ/2, the dark state is a symmetric superposition |Dnl>=(|eg>+|ge>)/√2, and the bright state |Bnl>=(|eg>-|gei) /√2 is an antisymmetric superposition. As shown in Figure 1, the phase and amplitude in the waveguide are plotted with red and blue shaded areas.

Furthermore, two directly coupled qubits with no separation along the propagation direction form an antisymmetric dark state |D1(2)>=(|eg>-|ge>)/√2 and a symmetric bright state |Bloc>=(|eg 〉+|ge〉)/√2. Compared to the waveguide-mediated coupling, the energy degeneracy of the bright and dark states is boosted by 2J, twice the coherent exchange coupling rate. As shown in Figure 1(c).

Then, as shown in Fig. 1(e), the two transmon bright states paired in situ interact through the waveguide to form a four-qubit dark state |D3> and a bright state |B4> with a decay rate of 4Γ. The paired dark states |D1>, |D2> stay in place and do not interact with the waveguide or the other pair.

Figure 1 Experiment overview

Figure 2 Experimental setup

Ultimately, this dark state's protection from decoherence results in decay times more than two orders of magnitude (about 500 times) greater than the waveguide-confined single qubit, in other words, a 500-fold improvement in qubit storage time.

This successful experiment lays the foundation for further research into dark states and their possible applications. For now, these studies are largely focused on fundamental research, and there are still many unanswered questions about the nature of these quantum systems. The concept of controlling the dark state proposed by the team can in principle be realized not only with superconducting qubits, but also on other technology platforms. Gerhard Kirchmair emphasizes: "The circuits we used function like artificial atoms and have advantages over real atoms, which are more difficult to strongly couple to the waveguide."

Link:

[1] https://www.nature.com/articles/s41567-022-01527-w

[2] https://www.sciencedaily.com/releases/2022/03/220314120718.htm