Controlling individual spins in the solid state is an important benchmark in the development of quantum information processing. The ability to initialize and readout the state of the spin as well as perform unitary rotations of that spin state are the necessary ingredients for full control of a single quantum state. All-optical approaches to these operations are promising as they provide a smaller footprint of control which could be used in photonic networks or spin arrays. However, traditional methods to fully control the spin of an NV center in diamond require disparate techniques. A distinct spin-selective intersystem crossing enables the spin to be both initialized and measured along its energy eigenstates. To take advantage of the quantum properties of the spin, microwave-frequency electron spin resonance techniques are then used to rotate the spin into and out of coherent superpositions of these eigenstates. Instead, we demonstrate a unified and all-optical technique to achieve full control of the spin that does not rely on any of the aforementioned methods. Using coherent light-matter interactions, we develop protocols for initialization, readout, and rotation of the NV center spin along any quantum basis by adapting techniques pioneered in atomic physics. These techniques take advantage of coherent dark states.
Coherent Dark States
Coherent dark states arise in a level configuration known as a Λ (lambda) system, which consists of two lower energy states coupled to a single higher energy, or excited, state. We form a solid-state Λ system within the NV center level structure by using two of the three ground state spin sublevels, mS = 0 and mS = +1, coupled to a spin-composite excited state level (see below, left). This spin-composite excited state is the result of an anticrossing between spin sublevels of the excited state. When optically driving transitions on resonance in this Λ system, the spin becomes trapped into a particular superposition of the ground state spin subspace, the “dark state,” through a dissipative process known as coherent population trapping (CPT). This dark state results due to destructive interference of the driving fields preventing excitation of the system. The specific dark state superposition is determined by the relative phase (φ) and amplitude (tan (θ/2)) of the driving fields, and can be chosen to lie anywhere on the Bloch sphere (see below, center). Similarly, we define the “bright state,” a ground state spin superposition orthogonal to the dark state, which couples very strongly to the driving fields. As such, the Λ system can be rewritten in terms of the bright and dark states with the driving fields recast as an optical pump along only the bright state transition (see below, right). These two states, bright and dark, form a fully selectable basis through which our protocols function. This definable basis obviates the need for any extra control steps to map a state to or from a preferred basis, such as the energy eigenstates.
All-Optical Control Protocols
Initialization of the spin into any state of our choosing is the result of the dissipative CPT interaction. Regardless of the prior state, the spin evolves toward the chosen dark state (seen below, left, in a tomographic Bloch sphere reconstruction). In addition, this process also provides a complementary readout protocol. The emitted photoluminescence during CPT is a measure of the projection of the spin state prior to the interaction along the dark/bright basis, where the number of photons is in direct proportion to the proximity of the state to the chosen dark state (i.e. a spin near the dark state emits few, while a spin near the bright state emits more) (see below, center, in a time trace of a 400 ns CPT interaction). A related technique, the product of stimulated Raman transitions (SRTs), occurs when we detune our driving fields. The resulting dispersive interaction produces an adiabatic shift of the bright state energy while the dark state energy remains unchanged. This energy shift manifests as rotation about the dark/bright state axis (see below, right, in a tomographic Bloch sphere reconstruction). All of these protocols can be performed along any dark/bright-state basis of our choosing.
All-Optical Spin Coherence Measurements
To demonstrate the impact of these protocols, we perform two all-optical measures of NV center spin coherence. We measure the inhomogeneous transverse spin coherence, or T2*, by varying the delay between two CPT pulses in a Ramsey sequence, in which the first pulse acts as an initialization onto the Bloch sphere equator, while the second acts as a readout along a particular axis of the equator (see below, left). We find T2* to be roughly 1 μs, which is corroborated by a similar measurement using electron spin resonance techniques. To measure the homogeneous transverse spin coherence time, T2, we combine all three techniques in a Hahn echo sequence, with an SRT pulse providing the “echo” between two CPT pulses for initialization and readout (see below, right). A measured T2 of roughly 900 μs is also corroborated by a similar electron spin resonance measurement.
This all-optical approach to single spin control is not limited to just the NV center. Unlike traditional techniques, which require the special spin-selective intersystem crossing to initialize and readout the spin, our techniques are more versatile and could be applied to a broader range of localized quantum states in solid-state materials, not just those with NV-like configurations.
To learn more about our studies, please refer to:
"All-optical control of a solid-state spin using coherent dark states", C. G. Yale*, B. B. Buckley*, D. J. Christle, G. Burkard, F. J. Heremans, L. C. Bassett, and D. D. Awschalom, Proc. Natl. Acad. Sci. USA 110, 7595 (2013). (*equal contribution)