Enhancing photon squeezing one leviton at a time

A mesoscopic device in the simple tunnel junction or quantum point contact geometry emits microwaves with remarkable quantum properties, when subjected to a sinusoidal drive in the GHz range. In particular, single and two-photon squeezing as well as entanglement in the frequency domain have been reported. By revising the photoassisted noise analysis developed in the framework of electron quantum optics, we present a detailed comparison between the cosine drive case and other experimentally relevant periodic voltages such as rectangular and Lorentzian pulses. We show that the latter drive is the best candidate in order to enhance quantum features and purity of the outgoing single and two-photon states, a noteworthy result in a quantum information perspective.

Figure 1

Schematic view of a two-filters setup designed to measure the dynamical response of the noise ${\mathcal{X}}^{\left(k\right)}$. A tunnel junction (yellow box) is driven by a time dependent voltage $V\left(t\right)$ and emits a current $i\left(t\right)$ which is split into two. The resulting contributions are filtered at frequency $\omega$ and $|k{\omega }_0-\omega |$, respectively (blue boxes). They are then multiplied among themselves and with a cosine signal ($\otimes$ symbols). The final output is then averaged over time.

Figure 2

Quadratures of the emitted electromagnetic field in units of $\mathcal{A}$, as a function of $q$ (number of injected electrons) and at zero temperature ($\theta =0$). Curves represent ${\langle B_{\text{lor}}^2\rangle }_c$ for the Lorentzian drive at $z=0.856$ and $\eta =0.1$ (full black curve), ${\langle A_{\text{lor}}^2\rangle }_c$ for the Lorentzian drive at $z=0.856$ and $\eta =0.1$ (red full curve), ${\langle A_{\text{cos}}^2\rangle }_c$ at $z=0.706$ for the cosine drive case (gray dashed curve), and ${\langle B_{\text{cos}}^2\rangle }_c$ at $z=0.706$ for the cosine drive case (orange dashed curve). Thin black horizontal line indicates the vacuum fluctuations (in units of $\mathcal{A}$). The choice of the parameter $z$ in each curve has been achieved by numerical minimization of the noise.

Figure 3

Value of the minimum of ${\langle B_{\text{lor}}^2\rangle }_c$ (Lorentzian drive, black squares) and ${\langle B_{\text{rect}}^2\rangle }_c$ (rectangular drive, red circles) in units of $\mathcal{A}$, as a function of $\eta$ and at zero temperature ($\theta =0$). They are compared with the theoretical minimum derived for a Dirac comb $4/{\pi }^2\approx 0.405$ (thin gray horizontal line) and the numerical minimum calculated for the cosine drive ($\approx 0.618$) (thin black horizontal line). The values of $z$ are different for each $\eta$ in order to maximize the squeezing ($z=z_{\min }$). Inset: Corresponding evolution of the value of $z_{\min }$ at which the minimum of the noise occurs (same color code and style for the points).

Figure 4

Evolution of the single-photon purity $\mu$ as a function of $\eta$ in the optimal squeezing configuration $\left[z=z_{\min }\left(\eta \right)\right]$ for a Lorentzian drive (red diamonds) and a rectangular pulse (blue triangles). Curves are compared with the optimal values calculated for a cosine ($\approx 0.931$, thin black horizontal line). The corresponding value for a square wave is obtained for the rectangular pulse at $\eta =1/2$.

Figure 5

Evolution of the two-photon purity ${\mu }_2$ as a function of $\eta$ in the optimal squeezing configuration ($z=z_{\min }$) for a Lorentzian drive (red diamonds) and a rectangular pulse (blue triangles). They are compared with the optimal values calculated for a cosine voltage ($\approx 0.917$, thin black horizontal line).