Individual nitrogen vacancy (NV) centers in diamond have proven to be robust spin-based quantum bits for studies of quantum information, towards applications in quantum technologies. While individual NV center spins can be initialized and read out optically, traditional photoluminescence-based spin readout techniques destroy (polarize) the spin during measurement. We circumvent this destructive readout method by coherently coupling light to an NV center, through which we can perform both non-destructive spin measurement and coherent spin manipulation via direct optical interactions. These interactions enable the coherent and reversible transfer of quantum information between NV center spins and photons for a number of potential applications in quantum information processing.
An energy level diagram of the NV center is depicted below, showing:
- Energy levels and resulting optical transitions:
An NV center can be optically excited from its spin-triplet orbital ground state to a spin-triplet, orbital-doublet excited state using green (532 nm) light. Most of the time, the NV center will subsequently decay back to the ground state through a phonon-assisted process by emitting a photon of lower energy (650 - 800 nm) which we then detect. The NV center can also absorb and emit photons resonant with the 637 nm orbital transition. The spin state of the NV center is generally preserved during these orbital transitions.
- Inter-system crossing decay mechanism:
Occasionally, the excited NV center decays through a set of orbital singlet states known as the inter-system crossing. This "dark" decay serves two purposes. First, it polarizes the spin into the ms = 0 spin state under optical illumination (because the ms = ±1 states are much more likely to decay along this pathway), which is used for qubit initialization. Second, its long decay lifetime creates a spin-dependent photoluminescence intensity under optical illumination, which is used for traditional readout of the spin state.
- Energy level fine structure (zoomed in):
The energies of the orbital-doublet (EX, EY), spin-triplet (ms = -1, ms = 0, ms = +1) excited state are stable at cryogenic temperatures (∼20 K and below) and are determined by the local strain and magnetic field experienced by the NV center. The fine structure depicted below results from an applied magnetic field of ∼1920 Gauss, and a transverse strain splitting of ∼16.5 GHz. The black double arrow denotes the EY, ms = 0 optical transition, which is roughly 3 GHz higher in energy (longer) than the EY, ms = -1 (magenta) optical transition.
When near-resonant light couples to an optical transition, both the optical transition and the light are modified in the form of an avoided level crossing. They form hybrid (or "dressed") spin-light energy eigenstates (|G> and |E>) that are shifted apart relative to their uncoupled values (colored in blue), as depicted on the left below for a single transition. The resulting energy shift (ε) of the occupied, ground-like hybrid state (|G>) is plotted on the right below as a function of the light's energy detuning (Δ) from optical resonance.
The near-resonant light we apply coherently couples to the electronic spin of a single NV center because the optical transition energies are spin-dependent. The resulting spin-light coupling serves two purposes. First, it shifts the polarization of transmitted light in a spin-dependent way via the Faraday effect, which we use for non-destructive spin readout. Second, the near-resonant light controllably modifies the electronic spin states of the NV center via the optical Stark effect, which we use for unitary spin manipulation. We probe these two effects independently in the same NV center using two different measurement sequences. By comparing both spin and light responses that result from their coupling, we are able to obtain deeper insight into the full interaction dynamics of the system.
Non-destructive single spin readout via the Faraday effect
We non-destructively read out the electronic spin state of an NV center via the Faraday effect. We first modulate the prepared spin state before exposing the NV center to near-resonant, tunable laser light and then we measure the resulting polarization modulation of the light from the Faraday effect. In addition to the Faraday phase shift, we also measure both absorption of the light using photoluminescence excitation (PLE) and the final spin projection (<SZ>) after the red laser is turned off using (destructive) spin-dependent photoluminescence from green laser excitation.
The timing sequence progresses as follows:
- Initialize spin into ms = 0
- Prepare spin with microwaves
- Alternate between preparing ms = 0 and ms = -1 spin states
- Interact with tunable red light
- Measure PLE intensity "IPLE"
- Measure the Faraday effect "phase shift"
- Measure final spin projection "<SZ>"
Below is the Faraday effect response and the PLE-measured laser absorption from a single NV center, measured as a function of laser detuning for a single optical transition. Also shown are fits to their expected functional form (grey curves).
We typically probe the optical transitions from two of the three spin states (ms = 0 and ms = -1) in a diamond NV center. Data from concomitant measurements of the Faraday effect (top), PLE-measured laser absorption (middle), and final spin projection showing red laser induced spin polarization (bottom) as a function of laser energy are shown below. These data were taken on an NV center with an orbital strain splitting of 16.5 GHz. The asymmetrical response between the EY, ms=0 transition (at 0 GHz) and the EY, ms = -1 transition (near -3 GHz) is an expected result of the spin-selective inter-system crossing decay mechanism.
Optical spin manipulation via the optical (AC) Stark effect
By using a different measurement sequence, we measure the spin rotations induced by the optical Stark effect. In the energy-level configuration of these experiments, the NV center spin rotates around the z-axis of the Bloch sphere defined for the ms = (0,-1) qubit basis. To measure this rotation, we prepare the spin along the Bloch sphere equator, in contrast to the Faraday effect measurements where the spin was prepared on the poles. To mitigate spin dephasing, we employ a modified Hahn echo sequence with phase control on the final pulse to measure multiple spin projections. The timing sequence (bottom) and Bloch sphere representation of the spin dynamics in the rotating reference frame (top) are depicted below.
For a given laser power and energy, the magnitude of spin rotation is proportional to the duration of the red laser pulse. This produces oscillations in the final spin projection as a function of laser pulse duration as depicted in the left graph below. The frequency and decay of these data give useful information about the strength and coherence of the spin-light interaction. For example, the NV center spin is rotated 180° along the Bloch sphere equator in 0.6 μs with a total fidelity of 89±1% in the particular dataset below (left). We also determine that the spin remains along the equator with 98.9±0.3% fidelity during this same 180° rotation from additional measurements (not shown). These fidelities set initial benchmarks on the interaction coherence between single NV center spins and light. Additionally, the spin rotation frequency from the optical Stark effect is proportional to the applied laser power for sufficient detuning (right graph). The red line in this graph is a linear fit to the data which crosses the origin.
Since the Faraday effect and optical Stark effect result from the same spin-light coupling, their responses are closely associated. Below is the Faraday effect phase shift superimposed with the appropriately-scaled spin rotation frequency from the optical Stark effect at the same laser power, all as a function of red laser energy. The blue arrow denotes the data point associated with the data shown in the above optical Stark effect oscillations. Plotting the data together in this way demonstrates that both the light and spin respond to each other in similar ways as a function of detuning.
The optical Stark effect spin response we measure decays due to decoherence and dephasing. Below is a graph of the number of spin rotations to 1/e decay as a function of detuning for data taken at two laser powers. The red curve is a simplified theoretical model of expected optical Stark effect coherence, accounting for laser intensity fluctuations and spectral hopping of the NV center optical transitions. The blue arrow denotes the decay of the optical Stark effect data shown 2 figures above.
In conclusion, we have coherently coupled the spin states of a single NV center to near-resonant laser light. With this spin-light coupling we have demonstrated both non-destructive measurements of a single NV center spin and unitary control of this same spin with light. These interactions enable coherent, reversible quantum information transfer between single NV center spins and light, which could be used in long-distance quantum communication and coupling of distant spins with light for quantum information processing technologies.
For more information, please see: "Spin-Light Coherence for Single-Spin Measurement and Control in Diamond", B. B. Buckley, G. D. Fuchs, L. C. Bassett, and D. D. Awschalom, Science 330, 1212 (2010). Originally published online in Science Express on 14 October 2010 (DOI: 10.1126/science.1196436). Direct Links: Abstract, Full Text (pdf).