Several teams have engineered detectors that are sensitive to single microwave photons by strongly coupling atoms (or qubits) to high-quality-factor (high-Q) cavities. This architecture, known as cavity quantum electrodynamics (cavity QED), can be used in various ways to detect photons. One destructive method measures quantum Rabi oscillations of an atom or qubit resonantly coupled to the cavity8,9,10. The oscillation frequency is proportional to , where n is the number of photons in the cavity, so this method essentially measures the time-domain swap frequency.

Another method uses a dispersive interaction to map the photon number in the cavity onto the phase difference of a superposition of atomic states . Each photon number n corresponds to a different phase φ, so repeated Ramsey experiments5 can be used to estimate the phase and extract n. This method is QND, because it does not exchange energy between the atom and photon. However, as the phase cannot be measured in a single operation, it does not extract full information about a particular Fock state |n〉 in a single interrogation. Nonetheless, using Rydberg atoms in cavity QED, remarkable experiments have shown quantum jumps of light and the collapse of the photon number by measurement5,12.

Here we report a new method that implements a set of programmable controlled-NOT (CNOT) operations between an n-photon Fock state and a qubit, asking the question ‘are there exactly n photons in the cavity?’ A single interrogation consists of applying one such CNOT operation and reading-out the resulting qubit state. To do this we use a quasi-dispersive qubit–photon interaction that causes the qubit transition frequency to depend strongly on the number of photons in the cavity. Consequently, frequency control of a pulse implements a conditional π rotation on the qubit—the qubit state is inverted if and only if there are n photons in the storage cavity. To ensure that this is QND, the qubit and storage cavity are adiabatically decoupled before carrying out a measurement of the qubit state.

To realize this method we extend circuit-based cavity QED (ref. 13) by coupling a single transmon qubit14,15 simultaneously to two cavities. In this scheme, the transmon qubit is used to interrogate the state of one cavity; then the transmon is measured with the other cavity. This separation of functions allows one cavity to be optimized for coherent storage of photons (high-Q) and the other for fast qubit readout (low-Q). Related work by Leek et al. 16 realized a single transmon coupled to two modes of a single cavity, where the two modes were engineered to have very different quality factors. A schematic of the two-cavity device is shown in Fig. 1a. The cavities are realized as Nb coplanar waveguide resonators with λ/2 resonances at ωs/2π=5.07 GHz and ωm/2π=6.65 GHz, respectively. The cavities are engineered, by design of the capacitors Cs and Cm, to have very different decay rates (κs/2π=50 kHz and κm/2π=20 MHz) so that the qubit state can be measured several times per photon lifetime in the storage cavity. By having these cavities at different frequencies, the fast decay of the readout cavity does not adversely affect photons in the storage cavity. A transmon qubit is end-coupled to the two cavities, with finger capacitors controlling the individual coupling strengths (gs/2π=70 MHz and gm/2π=83 MHz). The usual shunt capacitor between the transmon islands is replaced with capacitors to the ground planes to reduce direct coupling between the cavities. Furthermore, a flux bias line17 allows fast, local control of the magnetic field near the transmon. This facilitates manipulations of the detunings Δs=ωg,eωs and Δm=ωg,eωm between the transmon and cavities, where we use the convention of labelling the transmon states from lowest to highest energy as (g,e,f,h,…).

Figure 1: Circuit schematic and device.
figure 1

a, Circuit schematic showing two cavities coupled to a single transmon qubit. The measurement cavity is probed in reflection by sending microwave signals through the weakly coupled port of a directional coupler. A flux bias line allows for tuning of the qubit frequency on nanosecond timescales. b, Implementation on a chip, with a ωm/2π=6.65 GHz measurement cavity on the left and its large coupling capacitor (red), and a ωs/2π=5.07 GHz storage cavity on the right with a much smaller coupling capacitor (blue). A transmon qubit (green) is strongly coupled to each cavity, with gs/2π=70 MHz and gm/2π=83 MHz. It has a charging energy EC/2π=290 MHz and maximal Josephson energy EJ/2π≈23 GHz. At large detunings from both cavities, the qubit coherence times are T1T2≈0.7 μs.

To achieve high photon-number selectivity of the CNOT operations, there must be a large separation between the number-dependent qubit transition frequencies. To obtain this, we use small detunings (Δs/gs<10) between the qubit and storage cavity. Figure 2 shows spectroscopy in this quasi-dispersive regime as a function of flux bias when the storage cavity is populated with a coherent state . A numerical energy-level calculation is overlaid, showing the positions of various transitions. We define as the photon-number-dependent transition frequency |n,g〉→|n,e〉. Other transitions, such as |2,g〉→|0,h〉, are allowed because of the small detuning. Fortunately, we also see that the separation between and grows rapidly to order 2 gs=140 MHz as the qubit approaches the storage cavity.

Figure 2: Pulsed spectroscopy with a coherent state in storage cavity (〈n〉≈1) versus qubit–cavity detuning Δs=ωg,eωs.
figure 2

Calculated transition frequencies are overlaid in colour. The red and orange lines are the transitions of the qubit when n=0 and 1, respectively. Transitions to higher transmon levels (|f〉 and |h〉) are visible because of the small detuning. The arrow indicates the flux bias current used during the CNOT operations.

To test the photon meter, we generate single photons in the storage cavity with an adiabatic protocol. Our method uses the avoided crossing between the |0,e〉 and |1,g〉 levels to convert a qubit excitation into a photon. The preparation of a photon begins with the qubit detuned below the storage cavity (Δs−3gs), where we apply a π-pulse to create the state |0,e〉. We then adiabatically tune the qubit frequency through the avoided crossing with the storage cavity, leaving the system in the state |1,g〉. The sweep rate is limited by Landau–Zener transitions that keep the system in |0,e〉. The preparation protocol changes the qubit frequency by 600 MHz in 50 ns, giving a spurious transition probability less than 0.1% (calculated with a multi-level numerical simulation). This protocol actually allows for the creation of arbitrary superpositions of |0,g〉 and |1,g〉 by changing the rotation angle of the initial pulse. For example, if we use a π/2-pulse, after the sweep the system ends up in the state , where φ is determined by the rotation axis of the π/2-pulse. One could also use a resonant swap scheme, which has been successfully used to create Fock states9 up to |n=15〉. The method used here has the advantage of being very robust to timing errors.

After the photon is prepared in the storage cavity, the qubit frequency is adjusted such that Δs/gs5. At this detuning, the separation between and is 65 MHz. In Fig. 3a, we show pulsed spectroscopy at this detuning for several rotation angles of the initial preparation pulse. We observe well-resolved dips in the reflected phase of a pulsed signal sent at the measurement cavity frequency. The locations of these dips correspond to the qubit transition frequencies for n=0 () and n=1 (), and the relative heights match expectations from the different preparation-pulse rotations (for example, a π/2-pulse results in equal-height signals).

Figure 3: Single photon preparation and CNOT selectivity.
figure 3

a, Pulsed spectroscopy versus Rabi angle of the preparation pulse, showing the reflected phase of a pulse at the measurement cavity frequency after a 80 ns pulse near the qubit frequency. Traces are offset vertically for clarity and labelled with the rotation angle of the control pulse used in the preparation step. The dips correspond to ≈5.47 GHz and ≈5.41 GHz, respectively. b,c, Rabi driving the qubit transitions after preparing |n=0〉 (b) and |n=1〉 (c). The red (blue) traces show the measured qubit excited state probability after applying an interrogation Rabi pulse with varying angle at (). The residual oscillation of R1(θ) in c is mostly due to preparation infidelity.

To show selective driving of these transitions, we carry out Rabi experiments at and for the cases where we prepare |0,g〉 and |1,g〉. In each experiment we ensemble average measurements of the resulting qubit state after further decoupling the qubit from the storage cavity. For the |0,g〉 case (Fig. 3b) there is a large-amplitude oscillation when the drive is at (red, R0(θ)) and almost no oscillation when the drive is at (blue, R1(θ)). When we prepare |1,g〉 the situation is reversed (Fig. 3c); however, in this case the residual oscillation of R0(θ) (red) is substantial because of small errors in the preparation of |1,g〉 associated with the initial rotation of the qubit and, more importantly, the 10% probability of energy decay during the subsequent adiabatic sweep through the cavity.

The responses Ri(θ) are a result of driving and the far off-resonant drive of , where . The cross-talk is seen in the small residual oscillation of R1(θ) in Fig. 3b. In the Supplementary Information, we derive a method for extracting a selectivity and preparation fidelity from these data, giving a selectivity ≥95% for both interrogations and a preparation fidelity of |〈n=1|ψ〉|2≈88%. These numbers were confirmed by doing equivalent experiments over a range of preparation-pulse rotation angles between 0 and 2π (not shown).

If π-pulses are used in the interrogation step, measurement results of the average qubit state directly correlate with the probability of being in the states |n=0〉 or |n=1〉. Details of the scaling needed to do this transformation when the selectivity is <100% are presented in the Supplementary Information. These are the desired CNOT operations of the photon meter. If we now insert a variable delay before interrogating, we find that P0 (P1), the probability of being in |n=0〉 (|n=1〉), decays exponentially towards 1 (0), as shown by the red (orange) trace in Fig. 4b. The decay constant of T13.11±0.02 μs agrees with the linewidth of the storage cavity, 1/κs=1/(2π 50 kHz)=3.2±0.1 μs, measured in a separate, low-power reflection experiment.

Figure 4: Repeated measurements of photons.
figure 4

a, Experiment protocol. A microwave pulse and adiabatic sweep load a single photon into the storage cavity in the preparation step. This photon is interrogated repeatedly by number-selective CNOT gates on the qubit, followed by adiabatic decoupling, qubit readout and reset. b, Single and repeated interrogation after preparing |n=1〉 (top) or |n=0〉 (bottom), ensemble averaged over 50,000 iterations. The near-perfect overlap between single and repeated results demonstrates that the protocol is highly QND. The estimated uncertainty is the same for each point, so only a few representative error bars are shown for clarity (see Supplementary Information for error estimates). c, Transition probability diagrams for the interrogate n=0 (I0) and interrogate n=1 (I1) processes. We extract γ0(γ1)=1(10)±3% and δ0(δ1)=7(3)±3%.

Strong QND measurements are projective, such that if the measurement observable commutes with the Hamiltonian, the system will remain in an eigenstate of both operators between measurements. Consequently, comparing the results of successive interrogations provides a mechanism to test whether a particular protocol causes perturbations on the system beyond the expected projection. Here, we compare only ensemble average results, because the single-shot qubit readout fidelity for the device is 55%. This is sufficient to reveal processes that change the photon number, and technical improvements to interrogation speed or qubit readout fidelity should allow for real-time monitoring of the photon state.

The protocol cannot be repeated immediately, though, because the first interrogation may leave the qubit in the excited state. To circumvent this problem, we use the fast decay rate of the measurement cavity to cause the qubit to spontaneously decay into the 50 Ω environment. The ‘reset’ protocol brings the qubit into resonance with the measurement cavity for a time, τreset=50 ns, which is sufficient to reset the qubit with probability 98%. The procedure is described in detail in ref. 18.

After resetting the qubit, we can interrogate a second time. The full protocol for a repeated interrogation sequence is shown in Fig. 4a. The combination of a CNOT0 (CNOT1), a qubit measurement and a qubit reset define an interrogation process I0 (I1). Data for the four possible combinations of interrogating |n=0〉 and |n=1〉 are shown in Fig. 4b as a function of delay between the first and second interrogations. The data are ensemble averaged over all results from the first interrogation, so we do not observe projection onto number states. Instead, we again observe exponential decay, where the result of the second measurement is essentially indistinguishable from the first, indicating that the interrogation is highly QND.

Small deviations between first and second interrogations stem from finite photon lifetime in the storage cavity and non-QND processes that cause transitions to other photon numbers (Fig. 4c). A single interrogation process takes 550 ns, which accounts for the time gap between the single and repeated interrogation points in Fig. 4b. Recording the second interrogation results for different delays allows us to subtract the effect of photon T1 and calculate the transition probabilities for the I0 and I1 processes19. In principle, I0 and I1 can cause transitions to photon numbers outside the n{0,1} manifold; however, the absence of statistically significant deviations from P0+P1=1 suggests that any such effects are negligible. Instead, we consider only transitions from |n=1〉→|n=0〉 or |n=0〉→|n=1〉, characterized by the probabilities γi and δi, respectively, where i references the interrogation process I0 or I1. We observe γ0(γ1)=1(10)±3% and δ0(δ1)=7(3)±3%, demonstrating that this protocol is highly QND.

The protocol presented here is a fast and highly QND measurement of single photons, which we believe can be extended to detect higher photon numbers. It should be possible to demonstrate the projective nature of the interrogation and create highly non-classical states of light by post-selection, and eventually with higher fidelity readout it should be possible to observe quantum jumps of light in a circuit.