Quantum-Dot Single-Photon Sources for Entanglement Enhanced Interferometry

Multiphoton entangled states such as “N00N states” have attracted a lot of attention because of their possible application in high-precision, quantum enhanced phase determination. So far, N00N states have been generated in spontaneous parametric down-conversion processes and by mixing quantum and classical light on a beam splitter. Here, in contrast, we demonstrate superresolving phase measurements based on two-photon N00N states generated by quantum dot single-photon sources making use of the Hong-Ou-Mandel effect on a beam splitter. By means of pulsed resonance fluorescence of a charged exciton state, we achieve, in postselection, a quantum enhanced improvement of the precision in phase uncertainty, higher than prescribed by the standard quantum limit. An analytical description of the measurement scheme is provided, reflecting requirements, capability, and restraints of single-photon emitters in optical quantum metrology. Our results point toward the realization of a real-world quantum sensor in the near future.

Figure 1

(a) Two-photon excitation scheme via a virtual state (dashed line) and the cascaded emission of a pair of biexciton ($XX$) and exciton ($X$) single-photons with corresponding spectrum [only one of the two available recombination paths ($(|{\uparrow \Downarrow ,\downarrow \Uparrow ⟩}_{XX}\to |{\uparrow \Downarrow ⟩}_X\text{or}|{\downarrow \Uparrow }_Y\to |G⟩)$) is considered in the conducted experiment]. (b) Pulsed resonance-fluorescence of a charged exciton ($T$) in a quantum dot with corresponding spectrum. (c) Intrinsically phase-stable double-path Sagnac interferometer [15] with laser excitation scheme. First, beam splitter 2 (BS2) serves as the second part of an unbalanced MZI [with beam splitter 1 (BS1)] to generate the $|\mathrm{\Phi }{⟩}_2=(|20⟩+|02⟩)/\sqrt{2}$ state by exploiting two-photon interference at a position $\mathrm{BS}{2}^{\prime }$ [31]. The path-entanglement is then probed via phase-dependent autocorrelation measurements again on BS2, on a second interference position $\mathrm{BS}{2}^{\prime \prime }$. By rotating a phase plate (an ordinary glass plate in our case) in one of the arms, the relative phase difference $\phi$ between the two paths (blue dotted and solid lines) is varied. (d) Unfolded scheme of the photon path in the Sagnac interferometer.

Figure 2

Coincidence histogram simulation and data for the trion line. The black lines $C{l}_1$, $C{l}_2$, and $C{l}_3$ show the expected five peak clusters which are separated by the laser repetition period of 13.1 ns for a phase shift of $\phi =\pi /2$. In this special case the outcome is the same as for a typical Hong-Ou-Mandel experiment. The sum of these clusters ($\mathrm{\Sigma }C{l}_i$) displays the expected histogram which is in very good agreement with the measurement (top green line). The two green lines for phase shifts of $\phi =0$ and $\phi =\pi$ reflect measurement situations of constructive biphotonic interference.

Figure 3

Phase-dependent single-photon count rates (top row) and biphotonic coincidence rates (bottom row) for (a) $X$, (b) $XX$, and (c) $T$. Phase superresolution is achieved in all three cases. Insufficient two-photon interference visibility (e.g. $X$), or inadequate spatial mode overlap (e.g. $XX$) can prevent supersensitivity. On the contrary, the measurement using photons from the $T$ decay shows an improvement of phase precision beyond the standard quantum limit (see main text). Error bars represent the statistical error of the coincidence measurement.