Generating time-correlated photon pairs at the nanoscale is a prerequisite to creating highly integrated optoelectronic circuits that perform quantum computing tasks based on heralded single photons. Here, we demonstrate fulfilling this requirement with a generic tip-surface metal junction. When the junction is luminescing under DC bias, inelastic tunneling events of single electrons produce a stream of visible photons of plasmonic origin whose superbunching index is 17 (improved to a record of 70 by the authors during publication) when measured with a 53-ps instrumental resolution limit. The effect is driven electrically, rather than optically. This discovery has immediate and profound implications for quantum optics and cryptography, notwithstanding its fundamental importance to basic science and its ushering in of heralded photon experiments on the nanometer scale.
Tunnel junctions are important light sources in their own right that convert electric potential energy into photons, largely through one electron–one photon (1e− → 1γ) inelastic tunneling events. These junctions facilitate many intricate fundamental processes such as time-correlated two-electron tunneling (1, 2), overbias emission (3–5), photon antibunching in single-photon emitting molecular systems (6, 7), and photon bunching from dynamical processes that modulate junction properties, such as molecular motion (8, 9). These emission processes arise from how stochastic fluctuations couple to the electromagnetic modes of an environment (10), which imprint characteristic deviations away from Poissonian statistics onto the temporal correlations in the emitted photon stream. Critically missing from these examples is a 1e− → nγ process, where a single electron manifestly produces multiple photons. The simplest of these is the 1e− → 2γ process. Using scanning tunneling microscopy (STM)–induced luminescence techniques (11) to examine the light from atomically flat metal junctions, we detect a non-Poissonian process that manifests as photon superbunching, which, in tandem, evidences emission of time-correlated photon pairs from a tunnel junction formed between metals. The effect is reminiscent of two-mode squeezed photon pairs (12), but without externally applied AC voltages and the energy constraints imposed by millikelvin temperatures. Its detection now expands the inventory of fundamental processes that can be controlled in a tunnel junction environment.
The superbunching and its characterization are obtained with the experimental setup (13) shown in Fig. 1. The surface topography and spectroscopic characterization of a clean Ag(111) single crystal obtained with STM are shown in Fig. 2 (A and B, respectively). The light radiating from the junction (orange curve) due to the tunnel current is recorded while sweeping the bias from 1 to 10 V, holding the current constant with a feedback loop. The feedback causes the tip to retract from the surface in a step-like fashion (purple curve) due to field emission resonance (FER) states (green curve) at metal surfaces with a bandgap near the vacuum level (14). The succession of these FER states introduces oscillatory variations in the electronic density of states. Note that the total light emission intensity (orange curve) drops substantially from its maximum near 3 V when the voltage approaches the first FER state. Our measurement reproduces the essential, known features of a metal-metal tunnel junction (15, 16).
Light radiating from a junction formed between a gold tip and Ag(111) substrate travels along two optical paths (1, 2) through a series of lenses (L), viewports (V), and optical filters (F) to a pair of single-photon avalanche diodes (SPADs). The number of photon coincidence events as a function of time delay t between the SPADs, g(2)(t), is measured with a time-correlated single-photon counter (TCSPC). The voltage bias (U) is applied to the substrate. The tunnel current (I) is measured with a picoammeter (A). A third optical path to an optical spectrometer is not shown.
(A) Ag(111) surface topography with a monatomic step imaged at 3 V, 100 pA. X marks the position of bunching measurements. Scale bar, 5 nm. The gradation spans one 240-pm Ag terrace step height. (B) Total light intensity (orange), tip retraction (purple), and density of states (DOS; green) during a linear voltage sweep at constant current. The position of the first FER maximum is indicated with a black line. arb. units, arbitrary units. kcts, kilocounts. (C) An energy level diagram of an inelastic electron tunneling event leading to photon pair production. The junction is biased by a fixed Ubias voltage. An electron at the tip Fermi level (EF,tip) tunnels through a junction potential barrier U(z), where z is a position in the gap, arriving on the sample side with an energy E = e · Ubias above the sample Fermi level (EF,sample). E can be aligned or misaligned with FERs nearby. E is an upper bound for the total photon energy because metals provide a continuum of initial and final states.
The temporal photon intensity correlation function g(2)(t) that evidences photon superbunching is measured with a Hanbury Brown and Twiss interferometer (17) (Fig. 1) by collating the distribution of times t between one photon arriving at the start detector (single-photon avalanche diode 1 (SPAD 1)) and another photon arriving at the stop detector (SPAD 2) (6). Two photon counters are necessary to confirm simultaneously generated photons since the instrumental dead time is ~76 ns (see Materials and Methods). A temporal correlation event registers when both detectors sense one photon each, typically with a nanosecond time delay between the sensing. While accidental coincidences may occur at any relative time delay (as they involve uncorrelated photons), true coincidences require two emitted photons arriving simultaneously and manifest as a sharp feature in g(2)(t) at time zero. These special pairs can be produced according to the schematic shown in Fig. 2C. An inelastic tunneling process can excite tip-localized plasmon modes that subsequently decay into photons detected in the far field. In addition to well-known single-photon emission, bunched emission can occur whenever photon pairs are produced, such as in an idealized two-step cascade that produces one photon in each step (18).
Figure 3A shows the measured g(2)(t) for our tunnel junction light source derived from time-correlated single-photon counting, and plotted with coincidence events as a function of time between photon detection at the start and stop SPADs. Because the counting statistics of electron transport in a tunnel junction is Poissonian (19), the absence of an antibunching feature at time t = 0 is expected. However, the presence of a bunching feature is not. It signals that electroluminescence in a generic tunnel junction does not occur solely in the form of individual 1e− → 1γ events. While observing g(2)(0) > 1 is already indicative of bunched photon emission, g(2)(0) = 17 (also in Fig. 3A) shows that the photons are unambiguously superbunched (20). The existence of photon bunches containing at least pairs of photons is evidenced by the two independent SPADs detecting light within less than 53 ps of each other. While a bunch may contain more than two photons and may obey certain quantum mechanical relationships, these possibilities remain uncharacterized by the current experiment. Nevertheless, the high bunching ratio g(2)(0) is distinct from that generated by chaotic light sources, for which g(2)(t) ≤ 2 holds. The set point of 4.63 V, 20 nA is representative of a broad range of tunnel parameters where superbunching is observable. The bunching feature has an even narrower width than the reference correlation measured with light pulses from a picosecond white light source, thus indicating that the bunching peak shape is even closer to the instrumental response function than the reference measurement (blue curve in Fig. 3B; Materials and Methods). Thus, the peak value of g(2)(0) is limited by the detectors’ time resolution and may be substantially larger if detection with higher time resolution is used. Using g(2)(0) as a coincidence-to-accidental events ratio, this metric is already comparable to photon pair sources based on cooled optical fibers, which can perform quantum key distribution with a 3% bit error rate (21).