Quantum Erasure Using Entangled Surface Acoustic Phonons

Using the deterministic, on-demand generation of two entangled phonons, we demonstrate a quantum eraser protocol in a phononic interferometer where the which-path information can be heralded during the interference process. Omitting the heralding step yields a clear interference pattern in the interfering half-quanta pathways; including the heralding step suppresses this pattern. If we erase the heralded information after the interference has been measured, the interference pattern is recovered, thereby implementing a delayed-choice quantum erasure. The test is implemented using a closed surface acoustic wave communication channel into which one superconducting qubit can emit itinerant phonons that the same or a second qubit can later recapture. If the first qubit releases only half of a phonon, the system follows a superposition of paths during the phonon propagation: either an itinerant phonon is in the channel or the first qubit remains in its excited state. These two paths are made to constructively or destructively interfere by changing the relative phase of the two intermediate states, resulting in a phase-dependent modulation of the first qubit’s final state, following interaction with the half-phonon. A heralding mechanism is added to this construct, entangling a heralding phonon with the signaling phonon. The first qubit emits a phonon herald conditioned on the qubit being in its excited state, with no signaling phonon, and the second qubit catches this heralding phonon, storing which-path information which can either be read out, destroying the signaling phonon’s self-interference, or erased.

Popular Summary

In an interferometer, any information about which path a particle takes destroys the interference pattern, a fundamental result in quantum mechanics. A quantum eraser experiment tests whether the interference pattern can be recovered by erasing this information. Quantum erasers have been demonstrated using photonic interferometers. Here, we realize a quantum eraser using another medium: phonons, the quanta of mechanical vibrations.

Our experiment generates, for the first time, a two-phonon entanglement. We use a surface acoustic wave communication channel into which two qubits can emit and recapture itinerant phonons. The first qubit is controlled to release “half” a phonon, a superposition of states where either a “signaling phonon” is in the channel or the first qubit remains in its excited state. We interfere these paths by changing the relative phase of the two intermediate states, leading to constructive or destructive modulation of the qubit’s final state.

To determine whether the qubit remains in its excited state or a phonon is emitted, we realize another first: the qubit emits a “heralding phonon” in the absence of the signaling phonon. The heralding phonon, which carries the path information, is later captured by the second qubit, thus extinguishing the interference pattern. However, we show that the pattern can be recovered by erasing the information gained by the second qubit.

This experiment implements one of the milestone experiments of quantum optics, here using phonons, opening the door for realizing other phonon analogs of fundamental quantum-optics experiments. Perhaps in the future we will be able to listen to quantum music.

Figure 1

Experimental setup and quantum eraser scheme. (a) Two transmon superconducting qubits (blue) are coupled to a surface acoustic wave phononic channel (gray) via a central interdigitated transducer (IDT, green), using which both qubits can emit and capture itinerant phonons. The IDT is placed between two reflective mirror gratings (orange) that define a Fabry-Perot cavity and reflect phonons within the mirrors’ bandwidth back toward the IDT. Two tunable couplers (red) are used to dynamically control the coupling between the qubits and the IDT, allowing shaping the wave packets of emitted phonons, and ensuring their efficient reabsorption after completing the 500 ns acoustic round-trip. The couplers also enable the controlled partial release of phonons. (b) Optical micrograph of the device, showing (top) the acoustic Fabry-Perot structure on a lithium niobate chip, (bottom) the two superconducting qubits and associated superconducting wiring on a separate sapphire chip, and (middle) a side view of the flip-chip assembled device. (c) When one of the qubits ($Q_1$) swaps a half-phonon ($A$) into the acoustic channel, an interferometer can be implemented (green box): once $A$ completes a round-trip within the acoustic cavity, its reabsorption probability by $Q_1$ depends on the relative phase accumulated by $Q_1$ and $A$, and leads to interference in $Q_1$’s final excitation probability. To implement a quantum eraser, we generate an entangled phonon herald marking the which-path information by generating a second, entangled phonon ($B$) conditionally on $Q_1$ being in $|e⟩$ (blue box): this suppresses the interference. Capture and detection of the entangled herald $B$ by $Q_2$ acquires the which-path information after the interference of $Q_1$ and $A$ is complete, making this a time-delayed herald. Subsequently applying a $\pi /2$ pulse to $Q_2$ equalizes its $|g⟩$ and $|e⟩$ populations, erasing the which-path information and restoring the interference, thereby completing a delayed quantum eraser measurement.

Figure 2

Single-qubit frequency- and state-dependent energy decay. (a) We monitor the decay of $Q_1$’s state after excitation respectively to $|e⟩$ and $|f⟩$ [pulse sequence is in inset of (b)], dominated by emission of phonons into the IDT. $Q_1$’s coupler is set to maximum coupling and $Q_2$’s coupler is turned off. (b) Fitting the population evolution (see Ref. [40]) enables us to extract the transition rate ${\kappa }_{ge}$ of transition $g\text{−}e$ (blue) and the transition rate ${\kappa }_{ef}$ of transition $e\text{−}f$ (red) as a function of $Q_1$ frequency. The frequency dependence of each transition rate is seen to follow the frequency dependence of the IDT conductance (c). We identify two operating points ${\omega }_A$ and ${\omega }_B$. At frequency ${\omega }_{ge}={\omega }_A$, phonon emission on the $g\text{−}e$ transition dominates, resulting in phonon emission at ${\omega }_{ge}/2\pi =3.95\mathrm{GHz}$ within the mirror bandwidth (orange), while decay on the $e\text{−}f$ transition is suppressed. Similarly, at frequency ${\omega }_{ge}={\omega }_B=2\pi \times 4.15\mathrm{GHz}$, phonon emission on the $e\text{−}f$ transition dominates, resulting in phonon emission at ${\omega }_{ef}={\omega }_{ge}-|\alpha |=2\pi \times 3.97\mathrm{GHz}$ (gray dashed line), also within the mirror bandwidth, while decay on the $g\text{−}e$ transition is suppressed.

Figure 3

Which-path heralding. (a) After exciting $Q_1$ to $|e⟩$ with ${\omega }_{ge}=2\pi \times 3.95\mathrm{GHz}$, $Q_1$’s tunable coupling ${\kappa }_1$ is modulated dynamically to release a symmetric phonon wave packet with characteristic time $1/\kappa =15\mathrm{ns}$ on $Q_1$’s $g\text{−}e$ transition. The emitted phonon is later captured by $Q_2$ on its $g\text{−}e$ transition. (b) Inset pulse sequence: We initialize $Q_1$ to $|f⟩$ using two sequential pulses at the $g\text{−}e$ and $e\text{−}f$ transition, with ${\omega }_{ef}={\omega }_{ge}-|\alpha |=2\pi \times 3.97\mathrm{GHz}$. We then modulate ${\kappa }_1$ to emit a phonon on $Q_1$’s $e\text{−}f$ transition. The emitted phonon is later captured by $Q_2$ on its $g\text{−}e$ transition. During this process, $Q_1$’s $|g⟩$ population increases from 0 to 0.06 due to spurious relaxation from $|e⟩$ to $|g⟩$. Insets show the pulse sequences and schematics of the expected transfers. Open symbols represent the qubits’ populations measured at time $t$, dashed lines correspond to a numerical model taking into account the qubits’ decoherence and phonon losses.

Figure 4

Quantum eraser. (a) Pulse sequence: With $Q_1$ in $|e⟩$, its coupler is used to half-release a phonon at ${\omega }_A$ (blue). $Q_1$’s frequency is then detuned, accumulating a phase $\phi$ between the half-phonon and $Q_1$’s $|e⟩$ state. An optional $\pi$ pulse on $Q_1$’s $e\text{−}f$ transition (red) is followed by the coupler-controlled emission of a phonon at ${\omega }_B$ (orange), heralding that $Q_1$ is in $|e⟩$ and returning $Q_1$ to $|e⟩$. Following the optional heralding, $Q_1$ catches the half-phonon (blue) and is measured, completing the interferometry. Following $Q_1$’s measurement, $Q_2$ catches the optional heralding phonon (orange) and is measured at time $t_2=1.1\mu \mathrm{s}$. (b) Left: $Q_1$’s $|e⟩$ and $|f⟩$ state populations as a function of time $t$, showing the unheralded $P_e(t)$ for $\phi =0$ and $\phi =\pi$, which at time $t_1$ displays the interference maximum and minimum, and for the heralded $P_e$, which at time $t_1$ does not have a $\phi$ dependence. Also shown is $Q_1$’s $|f⟩$ state population when the herald is generated. Right: $Q_2$’s excited state $P_e(t)$ when the herald is generated, which ideally would reach the value $1/2$ but is limited by acoustic losses to ${\eta }_b\times 0.5\approx 0.32$. (c) Interference fringes $P_e(\phi )$ are visible when the herald is absent, but disappear when the herald reports which-path information ($Q_1$ in $|e⟩$). If the herald is generated but the information in $Q_2$ is erased, by applying a $\pi /2$ pulse on $Q_2$’s $g\text{−}e$ transition, the fringes reappear when $Q_1$’s measurement is conditioned on measuring $Q_2$ in $|e⟩$. This occurs even though $Q_1$’s measurement was already complete by the time the information in $Q_2$ is erased. (d) Probability of measuring $Q_2$ in $|e⟩$, showing lack of dependence on $\phi$. Also shown are variations in two-qubit probabilities $P_{gg}$, $P_{ge}$, $P_{eg}$, and $P_{ee}$. Inset shows the lack of variation of both qubits’ $|e⟩$-state probabilities $P_{e1}$ and $P_{e2}$ as a function of $\phi$ when applying the ${\pi }_{ef}$ pulse. Dashed lines in all panels correspond to a numerical model taking into account the qubits’ decoherence and phonon losses; see Ref. [40].