Degenerate Dark States Research Articles

Optical lattice with spin-dependent sub-wavelength barriers

We analyze a tripod atom light coupling scheme characterized by two dark states playing the role of quasi-spin states. It is demonstrated that by properly configuring the coupling laser fields, one can create a lattice with spin-dependent sub-wavelength barriers. This allows to flexibly alter the atomic motion ranging from atomic dynamics in the effective brick-wall type lattice to free motion of atoms in one dark state and a tight binding lattice with a twice smaller periodicity for atoms in the other dark state. Between the two regimes, the spectrum undergoes significant changes controlled by the laser fields. The tripod lattice can be produced using current experimental techniques. The use of the tripod scheme to create a lattice of degenerate dark states opens new possibilities for spin ordering and symmetry breaking.

Towards dark space stabilization and manipulation in driven dissipative Majorana platforms

We propose driven dissipative Majorana platforms for the stabilization and manipulation of robust quantum states. For Majorana box setups, in the presence of environmental electromagnetic noise and with tunnel couplings to quantum dots, we show that the time evolution of the Majorana sector is governed by a Lindblad master equation over a wide parameter regime. For the single-box case, arbitrary pure states (`dark states') can be stabilized by adjusting suitable gate voltages. For devices with two tunnel-coupled boxes, we outline how to engineer dark spaces, i.e., manifolds of degenerate dark states, and how to stabilize fault-tolerant Bell states. The proposed Majorana-based dark space platforms rely on the constructive interplay of topological protection mechanisms and the autonomous quantum error correction capabilities of engineered driven dissipative systems. Once a working Majorana platform becomes available, only standard hardware requirements are needed to implement our ideas.

Non-Abelian quantum adiabatic dynamics and phase simulation with classical resonant oscillators

It is known that the dynamics and geometric phase of a quantum system could be mapped mathematically into a classical system of coupled oscillators without loss of physics. In this work, we show that this quantum-classical mapping can also be used to simulate non-Abelian dynamics and phase of the quantum system with energy degeneracy by interpreting the quantum degeneracy as the resonance between the eigenfrequencies of the classical oscillators. The quantum evolution and Wilczek-Zee phase in the degenerate subspace can also be described by the classical non-Abelian evolution and a non-Abelian geometric angle in the resonant subspace. By studying the adiabatic evolution in this classical non-Abelian case, our results can also be used to generalize the concept of averaging principle and Hannay's angle into the classical system with resonant eigenfrequencies. The quantum-classical mapping of a tripod-scheme Hamiltonian with two degenerate dark states is employed to illustrate the classical non-Abelian dynamics and geometric angles.

Ultrafast Control of Excitonic Rashba Fine Structure by Phonon Coherence in the Metal Halide Perovskite CH_{3}NH_{3}PbI_{3}.

We discover hidden Rashba fine structure in CH_{3}NH_{3}PbI_{3} and demonstrate its quantum control by vibrational coherence through symmetry-selective vibronic (electron-phonon) coupling. Above a critical threshold of a single-cycle terahertz pump field, a Raman phonon mode distinctly modulates the middle excitonic states with persistent coherence for more than ten times longer than the ones on two sides that predominately couple to infrared phonons. These vibronic quantum beats, together with first-principles modeling of phonon periodically modulated Rashba parameters, identify a threefold excitonic fine structure splitting, i.e., optically forbidden, degenerate dark states in between two bright ones with a narrow, ∼3 nm splitting. Harnessing of vibronic quantum coherence and symmetry inspires light-perovskite quantum control and sub-THz-cycle "Rashba engineering" of spin-split bands for ultimate multifunction device.

Free energy for a damped cold atom in SU(2) non-Abelian gauge potentials

Our main aim in this work is to find out the exact formula of the equilibrium free energy for a cold atom subjected to a harmonic potential in the background of an artificial non-Abelian uniform magnetic field and linearly coupled to a heat bath. The heat bath consists of a collection of independent quantum harmonic oscillators, while its interaction with the cold atom is modeled in terms of bilinear coupling between the coordinate variables of the cold atom and the oscillators. The main thermodynamic properties of such a system are modified in comparison with the Abelian case. For a non-Abelian magnetic field generated from the laser methods employing degenerate dark states, we evaluate the effect of the non-Abelian dynamics on the magnetic moment of the cold atom.

Quantum adiabatic evolution with energy degeneracy levels

A classical-kind phase-space formalism is developed to address the tiny intrinsic dynamical deviation from what is predicted by Wilczek-Zee theorem during quantum adiabatic evolution on degeneracy levels. In this formalism, the Hilbert space and the aggregate of degenerate eigenstates become the classical-kind phase-space and a high-dimensional subspace in the phase-space, respectively. Compared with the previous same study by a different method, the current result is qualitatively different in that the first-order deviation derived here is always perpendicular to the degeneracy subspace. A tripod scheme Hamiltonian with two degenerate dark states is employed to illustrate the adiabatic deviation with degeneracy levels.

Parity-time symmetry in a flat-band system

In this paper we introduce Parity-Time ($\cal PT$) symmetric perturbation to a one-dimensional Lieb lattice, which is otherwise $\cal P$-symmetric and has a flat band. In the flat band there are a multitude of degenerate dark states, and the degeneracy $N$ increases with the system size. We show that the degeneracy in the flat band is completely lifted due to the non-Hermitian perturbation in general, but it is partially maintained with the half-gain-half-loss perturbation and its ``V" variant that we consider. With these perturbations, we show that both randomly positioned states and pinned states at the symmetry plane in the flat band can undergo thresholdless $\cal PT$ breaking. They are distinguished by their different rates of acquiring non-Hermicity as the $\cal PT$-symmetric perturbation grows, which are insensitive to the system size. Using a degenerate perturbation theory, we derive analytically the rate for the pinned states, whose spatial profiles are also insensitive to the system size. Finally, we find that the presence of weak disorder has a strong effect on modes in the dispersive bands but not on those in the flat band. The latter respond in completely different ways to the growing $\cal PT$-symmetric perturbation, depending on whether they are randomly positioned or pinned.

Non-Abelian geometrical control of a qubit in an NV center in diamond

We propose an approach for an optical qubit rotation in the negatively charged nitrogen vacancy (NV) center in diamond. The qubit is encoded in the ground degenerate states at a relatively low-temperature limit. The basic idea of the rotation procedure is the non-Abelian geometric phase in an adiabatic passage, which is produced by the non-adiabatic transition between the two degenerate dark states. The feasibility is based on the success of modeling the NV center as an excited-doublet four-level atom. By applying two pump and two Stokes laser pulses, we found that the behavior of the adiabatic passage depends crucially on the applied intensity of each applied laser field and the detunings between the laser frequencies and their corresponding atomic transition. Particularly, a non-adiabatic transition appears when the applied pump and Stokes laser pulses are off resonance with their corresponding atomic transition.

Quantum processing by adiabatic transfer through a manifold of dark states

We consider a network whose nodes are electromagnetic cavities, each coupled to a single three-level atom. The nodes are connected by optical fibers. Each atom is addressed by a control laser, which along with the cavity field drives atomic transitions. The network can be in the form of chain or two- and three-dimensional arrays of $N$ cavities connected by ${N}_{B}$ fibers. Following the work on a two-cavity system by Pellizzari, we find that under certain conditions the system possesses two kinds of dark states. The first kind are $N$ states corresponding to atomic excitations at each node and these are our logical states for quantum processing. The second kind are ${N}_{B}$ degenerate dark states on pairs of sites connected by a fiber. By manipulating intensities and phases of control lasers on the cavities, one can pass adiabatically among these dark states due to their degeneracy. This network operates as an $N$-level quantum system in which one can generate computationally useful states by protocols of external controls. We obtain numerical results for small chains and lattices to demonstrate some quantum operations such as the transport of states across the array, generation of $W$ states, and Fourier-like states. We also discuss effects of dissipation and limitations of the model.

Optical rotation of heavy hole spins by non-Abelian geometrical means

A non-Abelian geometric method is proposed for rotating of heavy hole spins in a singly positive charged quantum dot in Voigt geometry. The key ingredient is the delay-dependent non-Abelian geometric phase, which is produced by the nonadiabatic transition between the two degenerate dark states. We demonstrate, by controlling the pump, the Stokes and the driving fields, that the rotations about $y$- and $z$-axes with arbitrary angles can be realized with high fidelity. Fast initialization and heavy hole spin state readout are also possible.

Persistent currents in cold atoms

We propose a scheme to realize persistent mass and spin currents in cold atoms using optically generated gauge potentials. Two degenerate dark states can be created by coupling ``tripod'' atoms to three Laguerre-Gaussian laser beams carrying relative orbital angular momentum. Atoms in these dark states feel opposite effective magnetic fields of the flux-tube type and circulate in opposite directions around the axis of the tube, generating persistent mass currents in the system. Persistent spin currents can also be generated, with or without spin polarization.

Direct Observation of Dark Excitons in Micelle-Wrapped Single-Wall Carbon Nanotubes

We have performed electroabsorption spectroscopy on micelle-wrapped single-wall carbon nanotubes. In semiconducting nanotubes, many oscillating structures composed of the increase and decrease of absorption are observed in the spectra in the region of the first and second absorption bands, E11 and E22. The spectral shape is reproduced mainly by the second-derivative curve of the absorption spectrum, which indicates the presence of nearly degenerate bright and dark excitonic states.

运用“受激拉曼绝热通道”制备串行Λ系统相干叠加态

A scheme for creating an arbitrary coherent superposition of two atomic states in serial multi-\Lambda-type system is proposed. This technique with the application of a control field is based on the existence of two degenerate dark states and their interaction. The mixing of the dark states can be controlled by changing the relative delay time of the control pulse. One can get any desired superposition by changing the delay time of the control pulse.

Effects of an optically induced non-Abelian gauge field in cold atoms

We show that $N\ensuremath{-}1$ degenerate dark states can be generated by coupling $N$-fold degenerate ground states and a common excited state with $N$ laser fields. Interferences between light waves with different frequencies can produce laser fields with time-dependent amplitudes, which can induce not only $\mathrm{U}(N)$ non-Abelian vector fields but also the scalar ones for the adiabatic motion of atoms in such laser fields. As an example, a time-periodic gauge potential is produced by applying specific laser fields to a tripod system. Some features of the Landau levels and the ground-state phase diagram of a rotating Bose-Einstein condensate for a concrete gauge field are also discussed.

Dynamical evolution and analytical solutions for multiple degenerate dark states in the tripod-type atomic system

We study both dynamical and steady responses of a coherently driven four-level tripod-type atomic system, which may be either open or closed. With all three driving fields being on Raman resonance, this tripod system can quickly evolve into a complicated steady dark state decoupled from both coherent and dissipative interactions. In the open model, this tripod system is sensitive to all parameters in its dynamical evolution while the steady dark state only depends on the initial population distribution and the relative Rabi frequency values. In the closed model, however, relative values of spontaneous decay rates also play an important role in generating the steady dark state. Analytical results based on the quantum jump theory show that the steady dark state is always multiple (from twofold to sixfold) degenerate and usually comes into existence through both coherent and incoherent superpositions.

Non-Abelian Gauge Potentials for Ultracold Atoms with Degenerate Dark States

We show that the adiabatic motion of ultracold, multilevel atoms in spatially varying laser fields can give rise to effective non-Abelian gauge fields if degenerate adiabatic eigenstates of the atom-laser interaction exist. A pair of such degenerate dark states emerges, e.g., if laser fields couple three internal states of an atom to a fourth common one under pairwise two-photon-resonance conditions. For this so-called tripod scheme we derive general conditions for truly non-Abelian gauge potentials and discuss special examples. In particular we show that using orthogonal laser beams with orbital angular momentum an effective magnetic field can be generated that has a monopole component.

Adiabatic creation of coherent superposition states in atomic beams

We describe a technique for creating superpositions of degenerate quantum states, such as are needed for beam splitters used in matter-wave optics, by manipulating the timing of three orthogonally polarized laser beams through which moving atoms (or molecules) pass; motion across the laser beams produces pulses in the atomic rest frame. As illustrated with representative simulations for transitions in metastable neon, a single pass through three overlapping laser beams can produce superpositions (with preselected phase) of atomic beams differing by transverse momentum corresponding to the momentum of four photons. Like the two-photon momentum transfer of the tripod linkage pattern which it extends, the method relies on controlled adiabatic time evolution in the Hilbert subspace of two degenerate dark states. It is thus a generalization to multiple dark states (and larger transfers of linear momentum to the atomic beam) of the single dark state occurring with the stimulated Raman adiabatic passage (STIRAP) technique, and therefore it is potentially insensitive to decoherence due to spontaneous emission. By extending the tripod-linkage system to more numerous degenerate states, the technique not only increases the atomic beam deflections but, as we demonstrate, allows control over the superposition phase and amplitudes. LIke other techniques based on adiabatic time evolution, the technique is robust with respect to variations of the intensity, timing, and other characteristics of the laser fields. Unlike STIRAP, the same robust partial population transfer occurs for opposite timings of the pulse sequence, as is needed for such procedures as Hadamard gates.

Coherent population transfer and superposition of atomic states via stimulated Raman adiabatic passage using an excited-doublet four-level atom

Coherent population transfer and superposition of atomic states via a technique of stimulated Raman adiabatic passage in an excited-doublet four-level atomic system have been analyzed. It is shown that the behavior of adiabatic passage in this system depends crucially on the detunings between the laser frequencies and the corresponding atomic transition frequencies. Particularly, if both the fields are tuned to the center of the two upper levels, the four-level system has two degenerate dark states, although one of them contains the contribution from the excited atomic states. The nonadiabatic coupling of the two degenerate dark states is intrinsic, it originates from the energy difference of the two upper levels. An arbitrary superposition of atomic states can be prepared due to such nonadiabatic coupling effect.

Preparation of Fock states and quantum entanglement via stimulated Raman adiabatic passage using a four-level atom

We study the behaviour of an atom-cavity system exposed to a stimulated Raman adiabatic passage (STIRAP) process in a four-level system, with a coupling scheme which generate two degenerate dark states. We find that the non-adiabatic interaction of the two dark states guarantees that the cavity Fock states can always be generated by both intuitively and counterintuitively ordered pulses. Furthermore, we propose a method to entangle two atoms. Depending on the ordering of the pulses two orthogonal entangled states can be prepared. Since these entangled states do not have component of the excited states included, the technique is robust against the detrimental consequences of spontaneous emission.

Novel laser controlled variable matter wave beamsplitter

We demonstrate a novel variable beam splitter using a tripod-linkage of atomic states, the physics of which is based on the laser control of the non-adiabatic coupling between two degenerate dark states. This coupling and the splitting ratio is determined by the time delay of the interaction induced by two of the laser beams.