A fluorescent-protein spin qubit

Abstract

Quantum bits (qubits) are two-level quantum systems that support initialization, readout and coherent control¹. Optically addressable spin qubits form the foundation of an emerging generation of nanoscale sensors^2-7. The engineering of these qubits has mainly focused on solid-state systems. However, fluorescent proteins, rather than exogenous fluorescent probes, have become the gold standard for in vivo microscopy because of their genetic encodability^8,9. Although fluorescent proteins possess a metastable triplet state¹⁰, they have not been investigated as qubits. Here we realize an optically addressable spin qubit in enhanced yellow fluorescent protein. A near-infrared laser pulse enables triggered readout of the triplet state with up to 20% spin contrast. Using coherent microwave control of the enhanced-yellow-fluorescent-protein spin at liquid-nitrogen temperatures, we measure a (16 ± 2) μs coherence time under Carr-Purcell-Meiboom-Gill decoupling. We express the qubit in mammalian cells, maintaining contrast and coherent control despite the complex intracellular environment. Finally, we demonstrate optically detected magnetic resonance in bacterial cells at room temperature with contrast up to 8%. Our results introduce fluorescent proteins as a powerful qubit platform that paves the way for applications in the life sciences, such as nanoscale field sensing and spin-based imaging modalities.

Fig. 1. Photophysics of EYFP proteins and OADF readout scheme.

a, Concept of EYFP-based sensing approach. Left: a fusion protein consisting of an EYFP qubit conjugated to a target protein (grey). As an illustrative example, the structure of an EYFP–glutaredoxin fusion protein is shown. Genetic encoding ensures that every target protein is within a few nanometres proximity of exactly one EYFP sensor qubit. Right: to enhance sensitivity, an ensemble of fusion proteins within the optical excitation volume is probed. It is noted that, in this paper, we limit ourselves to investigating the physics of EYFP and not actual fusion proteins. b, Energy-level diagram of EYFP with OADF readout scheme. c, The natural transition orbital structure for the T1 state, calculated by ab initio calculations. d, Raw photoluminescence (PL) signals (top) and PL contrast (bottom) of OADF-based spin readout as a function of time after the onset of the 912-nm laser pulse for a π-pulse on the T_x–T_z (purple), T_y–T_z (blue) transition and the OADF signal with no microwave pulse (grey). The measurement sequence above the figure illustrates the timing of the microwave and optical pulses. The ‘detector’ channel represents the timing of the acousto-optic modulator used to gate the detector. Panel d is measured at 80 K.

Fig. 2. ODMR spectroscopy of EYFP.

a, Experimental ODMR signal as a function of externally applied magnetic field. The faint resonance (indicated by the asterisk) at approximately ω = (2π) × 0.9 GHz is associated with microwave harmonics that drive the T_x–T_z and the T_y–T_z transitions. b, Simulated ODMR response based on the model from equation (1). The fit parameters (D, E, linewidth of resonance, and the T_x–T_z and the T_y–T_z amplitudes) are extracted from an ODMR measurement at low magnetic fields (Methods). The ODMR amplitude for the T_x–T_y transition is set to 0. c, Experimental (green and purple) and simulated (black) ODMR spectrum at 4.2 mT and 34.1 mT. Panels a and c are measured at 80 K.

Fig. 3. Coherent control of EYFP qubits.

a, Rabi oscillations of EYFP T_x–T_z transition driven at a frequency of (2π) × 2.815 GHz. The fit corresponds to an exponentially damped cosine (black). b, Spin coherence as a function of total evolution time (T_Hahn) under Hahn-echo decoupling for different magnetic fields, with stretched-exponential fits. Inset: the scaling of the Hahn-echo dephasing rate ($1/T_2^{\mathrm{H}\mathrm{a}\mathrm{h}\mathrm{n}}$) as a function of external magnetic field and the corresponding theoretical model (black). c, The same as in b but under a CPMG decoupling sequence for different numbers of π-pulses (N) and no external field. Inset: $T_2^{\mathrm{CPMG}}$ scaling as a function of N and its corresponding fit (black). d, Contrast as a function of evolution time (T_relax) for different sample temperatures fit to exponential decays. Inset: the spin-lattice relaxation time (T₁) as a function of temperature fitted with 1/T₁ = AT + BT⁷, with fitted amplitudes A = 43 ± 8 K⁻¹ s⁻¹ and B = (47 ± 7) × 10⁻¹² K⁻⁷ s⁻¹. In all plots, grey data points indicate additional measurements shown in the inset but not the main plot for clarity. The fit errors in the insets of c and d are smaller than the data points and omitted. Panels a–c are measured at 80 K.

Fig. 4. Room-temperature quantum sensing.

a, Contrast of OADF-based spin readout as a function of time after the onset of the 912-nm laser pulse for the T_x–T_z (purple) and the T_y–T_z (blue) transition. b, ODMR in aqueous solution at various magnetic fields. The red points indicate the frequencies of the field sensing experiment in c. c, DC magnetic-field sensing operating at a bias field of 36.5 mT by measuring the difference in the ODMR contrast defined as C_T = [PL_sig(ω_a) − PL_sig(ω_b)/PL_back]. The measurement is performed at the two frequencies ω_a = (2π) × 3.54 GHz and ω_b = (2π) × 3.43 GHz indicated in b. PL_sig(ω), the OADF signal at a microwave frequency (ω); PL_back, the OADF signal in the absence of a microwave drive. Panels a–c are measured at room temperature.

Fig. 5. Coherent control in cells.

a, A wide-field fluorescence image of HEK 293T cells expressing cytosolic EYFP (blue). A loop structure for applying the microwave drive is visible. ODMR scans in b are measured in the white outlined regions, and OADF is thresholded for the brightest pixels (red). Scale bar, 100 μm. b, ODMR signal averaged over the bright pixels (red, on cells) and dark pixels (purple, off cells). Instead of contrast, the PL difference normalized to the number of pixels is shown to illustrate the size of the signal contributed by the background. c, Rabi oscillations of T_x–T_z transition driven at (2π) × 2.835 GHz measured with the same process as in b. d, ODMR spectra of EYFP measured on E. coli cells. The wide-field image in a is measured on HEK cells at room temperature. The red pixel overlay in a is measured on HEK cells at 175 K. b and c are measured at 175 K. Panel d is measured on a pellet of E. coli at room temperature.

Extended Data Fig. 1. Comparison of different sensing platforms.

The x-axis indicates the distance between the qubit and the target molecule, and the y-axis indicates the sensor sensitivity. Circles (and star) indicate systems that have been delivered into cells. Open boxes denote systems that have not been delivered into cells. Typical state-of-the-art sensitivities for vapor cells (green)^–, SQUIDs (brown)^–, Nitrogen-vacancy centres in bulk diamond (blue boxes)^,–, Nitrogen-vacancy centres in nanodiamonds (blue circle)^,–, and molecular qubits in a non-aqueous host (red boxes)^, are indicated. An ensemble of $773\times {10}^6$ EYFP molecules in aqueous solution (i.e., this work) is indicated by a star. The red circle indicates the projected sensitivity of a single EYFP protein. We note that in a fusion protein the relevant length scale determining the sensitivity is the separation of the EYFP protein to the target protein (i.e., the size of the EYFP protein) and not the diffraction-limited excitation volume.

Extended Data Fig. 2. Experimental setup.

488 nm and 912 nm diode lasers are gated using acousto-optic modulators (AOMs) and coupled into single-mode fibres. The fibres deliver laser light to a movable optical assembly for scanning over the sample. Dichroic mirrors overlap the excitation beams such that they are focused to the same spot by the microscope objective (60x magnification, 0.7 numerical aperture). The optical powers at the back of the objective for the 488 nm and 912 nm lasers are about 0.4 mW and 65 mW, respectively. Light collected from the sample passes through the dichroic mirrors and filters for removing the laser light, and is focused onto a single-mode fibre. The fibre acts as a pinhole, filtering out-of-focus light such that the signal is primarily from proteins illuminated with the highest laser intensities. After being gated by an AOM, the collected light is detected by a single-photon counting module or, in Extended Data Fig. 3a, a spectrometer. The sample is mounted in a custom imaging cell that holds 5 μl. It encapsulates the sample between two 500 μm thick sapphire windows, sealed by an o-ring. The sapphire substrate nearer to the cryostat window is photolithographically patterned with microwave loop structures using a lift-off process. The cryostat is evacuated to < 1 Torr and subsequently cooled following a temperature profile similar to Extended Data Fig. 4b. An external DC magnetic field is applied using a permanent magnet attached to a motorized translation stage outside of the cryostat. The microwave output of the RFSoC is fed into a series of amplifiers before being delivered to the loop structures. The microwave power before entering the cryostat was approximately 1 W.

Extended Data Fig. 3. Triplet state readout.

a, The EYFP initialized with a 488 nm laser pulse, then the spectra of the collected light recorded during a subsequent 912 nm laser pulse (purple), as well as the fluorescence collected during continuous illumination with the 488 nm laser (green and red). b, After initialization, the time trace of the collected light as a function of time after the onset of the 912-nm laser pulse without (grey), and with (purple) a microwave π-pulse on the T_x−T_z transition. c, The same as b, but on the T_y−T_z transition (blue). Panels b and c are measured at 80K and display similar data as Fig. 1d but over an increased time range.

Extended Data Fig. 4. Sample integrity.

a, Circular dichroism measurement taken on protein just after expression (before cooling), and after a full measurement sequence consisting of loading into the sample holder, cooling to cryogenic temperatures, and warming back up to room temperature (after cooling). b, Cooling profile of the cryostat platform. c, Bleaching lifetime of the protein versus laser power measured at the back of the objective. Panel a was measured at room temperature and c was measured at 4 K.

Extended Data Fig. 5. Resonance frequencies vs. magnetic field.

Histogram of randomly oriented molecules’ resonance frequencies as a function of applied magnetic field using the Hamiltonian in eq. 1. Some molecules’ T_y−T_z and T_x−T_y transitions overlap at higher applied magnetic fields.

Extended Data Fig. 6. Calculated D and E parameters.

The calculated |D| and |E| parameters using TDDFT with B3LYP-optimized geometries and various functionals along with the experimentally measured values.

Extended Data Fig. 7. Rabi oscillation decay.

a, Simulation of the magnetic flux density and field vectors generated from an omega waveguide. The field inhomogeneity across our optical spot at the centre is negligible (< 2%). b, Experimentally observed Rabi oscillations fitted with a solid black line. The decay of the higher (lower) power Rabi oscillation is 18 ns (51 ns) and illustrated by a dashed black line. c, Simulated average population of an ensemble of randomly oriented molecules assuming a linewidth (2π) × 33 MHz. The decay of the higher (lower) power Rabi oscillation is 38 ns (77 ns) and illustrated by a dashed black line. The corresponding distributions of Rabi rates are shown in the inset. d, Damped cosine fit parameters of the simulated Rabi oscillations. We note that the powers reported in the legends of b and c are not relative to each other. Panel b is measured at 80 K.

Extended Data Fig. 8. YZ transition at room temperature.

ODMR spectra of the T_y−T_z transition at room temperature, exhibiting a broadened linewidth with an applied magnetic field.

Extended Data Fig. 9. Knife-edge measurements.

In order to characterize the optical beam morphology, the microscope optical assembly is positioned to focus the 488 nm laser spot on a set of optical windows outside the cryostat that mimic the measurement conditions. The power transmitted through a photolithographically-patterned metal edge in the sample plane is measured as a function of transverse displacements in X axis a and Y axis b. This measurement is repeated for various axial displacements. The power versus transverse position is fitted to an error function. The beam diameter extracted by the error function fit is then examined as a function of axial displacement (inset). A fit to a hyperbolic profile allows for the extraction of the beam waist and Rayleigh range. The beam appears to display coma or spherical aberration, as well as astigmatism. These aberrations are likely the result of errors in alignment through the cryostat window and sample coverslip.

Extended Data Fig. 10. Sensitivity estimation.

a, Residuals from Fig. 4c used to estimate the DC sensitivity at room temperature. b, CPMG sequence used for AC magnetic field sensing. c, $n_{\mathrm{\Delta },250k}$ and its fit (black). d, The residuals estimated from $n_{\mathrm{\Delta },250k}$ and its fit. e, The estimated η. Panel (c) is measured at 80 K.

Extended Data Fig. 11. Cell measurements.

a, Brightfield image corresponding to Fig. 5a. b, Brightfield image of loop structure scanned in Fig. 5c to measure Rabi oscillations. c, Confocal fluorescence image of a. d, OADF signal acquired during ODMR scan of selected areas in c. e, Same as Fig. 5a. f, Same as c but on the loop structure in b. g, Same as d but corresponding to f. h, Same as e but with the thresholded pixels in g. Panels a, b, e, h were taken at room temperature. Panels c, d, f, g, and the red highlighted pixels in e, h were taken at 175 K.

Extended Data Fig. 12. Mechanism of room temperature ODMR.

a, Widefield fluorescence image of E. coli expressing EYFP that was measured in Fig. 5d. The red dot marks the measurement position. b, Readout contrast as a function of time after the onset of the 912 nm readout pulse when it is applied 10 μs after the 488 nm laser pulse ends. A 100 ns microwave pulse is applied 100 ns after the onset of OADF. c, Readout contrast as a function of time after the onset of the 912 nm readout pulse when the microwave drive and readout laser have no temporal overlap. A 100 ns microwave pulse at (2π) × 2.79 GHz is applied immediately after the 488 nm pulse. A 100 ns delay between the microwave pulse and 912 nm readout pulse ensures no temporal overlap.