Quantum Dot Single-Photon Source Characterization Using High-Precision Timing Electronics | Swabian Instruments Time Tagger & Pulse Streamer

A quantum dot (QD) is a quantum emitter that is artificially created when all three dimensions of a material are comparable to or smaller than the electron’s de Broglie wavelength, which resembles the spatial extent of a single electron. Reducing the size of a solid-state material below the de Broglie wavelength in a certain dimension alters the density of states of the electronic wavefunction, as the latter is now confined to two dimensions, creating a quantum well. Shrinking down another dimension of the material leads to a 1D quantum wire.

A quantum dot (QD) is obtained when all three dimensions are comparable or below the electron’s de Broglie wavelength, as depicted in Fig. 1. This 0D quantum material now shows an atom-like density of state or energy spectrum with distinct peaks referring to electronic transitions from the valence to the conduction band. By tuning the size, the energy or wavelength of the transitions can be widely tuned over the entire optical domain from the UV to the IR.

Quantum Dots, also known as artificial atoms, exist in various shapes and materials, where the most prominent can be classified into semiconductor epitaxial Quantum Dots (eQD), colloidal Quantum Dots (cQD), and carbon-based Quantum Dots (CQD). They all have in common that the spatial extent of the QD is in the order of a few to a few tens of nanometers to reach the confinement of the electronic wavefunction. This quantum confinement results in different material behaviours and new electronic and optical properties, and the creation of structures resembling atoms, leading to the term “artificial atoms”.

In general, quantum confinement encompasses photon absorption in the near UV or visible spectra and a powerful emission across the visible to NIR spectrum with high quantum yield. Smaller QDs emit shorter wavelengths (blue light) or higher energy than larger QDs (red light), resulting in size-dependent wavelength emissions. Their electronic and optical properties can be tuned in various ways by choosing different semiconductor materials, QD shapes, or surface terminations. These features give Quantum Dots a strong potential for revolutionizing various technologies like energy harvesting, bioimaging, medicine, display, camera technologies, and laser development. Especially for emerging quantum information technologies, QDs are promising candidates for quantum light generation, such as single-photon sources (SPS) and entangled photon-pair sources ².

In the early 2000s, traditional inorganic QD raised toxicity concerns, resulting in the emergence of carbon-based QDs (CQDs) as a less toxic, more biocompatible, lower-cost alternative with simpler synthesis and waste management procedures. CQDs’ biocompatibility, size, and efficiency as photocatalysts and electrocatalysts make them particularly suitable for energetic applications and ecosystem management. Within the biomedical sector, CQDs are particularly useful for drug development, tumor bioimaging, and targeted therapeutic treatments such as photothermal therapy. Efficient drug delivery of CQDs can be monitored in real-time via Förster Resonance Energy Transfer (FRET) techniques. FRET-based techniques have also been utilized to investigate optical properties, fluorescence quenching, or transfer of photo-induced electrons, toward the development of Carbon-Based Quantum Dot optical sensors.

One of the many promising applications of QDs is their use as single-photon sources (SPS) for quantum information experiments. An SPS is a true quantum light source that deterministically emits just a single quanta of light within a given time window. For example, certain approaches to photonic quantum computing need an SPS to generate the input states for the computation unit ³. Further, secure communication via quantum key distribution (QKD) often uses single photons as flying qubits to transmit the quantum information from the sender to the receiver. Depending on the protocol used for QKD, pairs of entangled photons need to be exchanged between sender and receiver. So far, most experiments rely on spontaneous parametric down conversion (SPDC), a process in which a nonlinear crystal generates these photon pairs or heralded single photons. However, the drawback of using this method is that down conversion is a probabilistic process with a low success rate and hence a low photon pair generation rate.

Quantum Dots can overcome this limitation introduced by Spontaneous Parametric Down Conversion (SPDC), since they are pumped electrically or by a laser pulse and deterministically emit a single photon or photon pair within a short time window (typically a few ns). Thus, they represent a pulsed, deterministic SPS or entangled photon pair source (Fig. 2).

Timing electronics are crucial for QD characterization techniques, facilitating the accurate determination of their emission properties, lifetimes, and quantum yield. To study the brightness, indistinguishability, and purity of a QD single photon source, time-correlated single photon counting (TCSPC) experiments are necessary:

• Brightness: Defined as the probability of getting a photon per excitation pulse. It connects to the photon flux emitted by the SPS, i.e., the rate of single photons that can be emitted (Fig. 2). This parameter is determined by the spontaneous emission lifetime of the excited state and the pulse repetition rate of the pump, where the QD emission is collected by a single photon detector (SPD) and the time-to-digital converter (TDC) calculates the photon count rate from which the brightness can be inferred. A Lifetime Histogram can then be calculated from collecting the time differences between the excitation (“start”) and photon detection by the SPD (“stop”). Since the lifetime is quite short (typically 100s of ps to a few ns) in comparison to other quantum emitters, Quantum Dots show a high brightness and are well-suited as an SPS. A digital pulse pattern generator can be leveraged to trigger the laser and serve as a start signal for the histogram calculation.

• Indistinguishability: Refers to the wavelength and spectral width of the emitted photons, which should be the same for each photon emitted by the QD (Fig. 2). This is characterized using an unbalanced Mach-Zehnder interferometer and two SPDs (Fig. 3b). If one arm of the interferometer delays the first photon by the laser pulse repetition time, it can interfere at the second beam splitter with a second photon of the next pulse. If both photons are indistinguishable, quantum mechanics predicts both photons to leave the beam splitter on the same output port. Therefore, the timing electronics, in theory, never detect a coincidence between both SPDs clicking. This process is called Hong-Ou-Mandel (HOM) interference, and it receives its name from the three scientists who theoretically discussed and experimentally defined this effect for the first time. In reality, dark counts and background light lead to coincidence clicks, but the higher the HOM visibility, the higher the indistinguishability of the QD.

• Purity: Characterizes how close the QD emission comes to an ideal SPS in terms of the number of photons emitted per pulse. Ideally, there should be exactly one photon in every pulse time window. However, losses and background light lead to the emission of no or multiple photons within a pulse (Fig. 2). It is determined using a Hanbury-Brown-Twiss (HBT) intensity interferometer (see also Intensity Interferometry ), which consists of a 50:50 beam splitter and two SPDs connected to the TDCs (Fig. 3b). Here, the time delay between the clicks on both detectors is measured and histogrammed to give the $g^{(2)} (\tau)$ correlation function. For an ideal SPS, the latter shows a dip at zero time delay $(\tau=0)$, indicating that only one photon at a time arrives at the detectors. The closer the value of $g^{(2)} (0)$ comes to zero, the higher the purity of the QD.

In addition to the set of measurements presented above, time-correlated single photon counting (TCSPC) also plays a key role in investigating the following characteristics of Quantum Dots:

• Photostability Assessment: TCSPC facilitates the observation of numerous decay components and emission states, therefore enabling the evaluation of photoluminescence complex decay kinetics of QDs. Overall, this facilitates a quantitative evaluation of photobleaching kinetics, a better understanding of photophysical processes, and advances the development of more stable QD materials for long-lasting applications.

• Quantum Dot Emission Influencing Factors: TCSPC provides information on lifetimes, photon correlation properties and behaviors, and fluorescence spectra. This technique aids in identifying surface traps, defects, and other factors that influence QD emission, providing expertise to engineer QDs with enhanced emission properties.

• Blinking assessment: TCSPC is used for monitoring and characterizing the on-off dynamics of QD emission, facilitating the study of stochastic switching between bright and dark states (“blinking”). A better understanding of the underlying mechanism can help enable strategies to mitigate or control blinking effects, which is crucial for single-photon sources and imaging applications.

Time-correlated single photon counting (TCSPC) is a powerful method for deciphering the complex optical attributes of quantum dots. Its capacity to provide event timing information of photon emissions is crucial for a wide variety of QD applications and characterization methods.

On the acquisition side, the high demands of Quantum Dot characterization experiments typically result in limitations from the timing electronics or time-to-digital converter (TDC) side, including:

• Insufficient precision: The lifetime of Quantum Dots is relatively short compared to other quantum emitters and lies in the range of a few hundred picoseconds to a few nanoseconds ^{5 6}. To resolve such short lifetime decays, the timing jitter of the detector as well as the TDC has to be at least an order of magnitude lower than the lifetime. The same argument applies to the measurement of the HOM interference dip and the purity measurement. Here, values up to 95% for the HOM visibility and purities above 90% i.e., $g^{(2)} (0) <0.1$ have been measured ⁵.

• High count rates cannot be captured: Single photon emission rates of a few Mcounts/s associated with the typical brightness values of quantum dots (10-20%) ⁵ require timing electronics with sufficient input frequency, data transfer rate, and processing capabilities.

• Low digital resolution and insufficient software capabilities: To obtain well-resolved datasets of the lifetime, HOM dip, and the purity measurements, the TDC needs to be able to generate (correlation) histograms with a fine binning down to a picosecond resolution.

On the signal generation side, a digital pulse pattern generator with insufficient features can be limiting in performing the signal streaming, suffering from:

• Lack of ability to generate high-frequency trigger signals: The short Quantum Dot lifetime allows for high repetition rates of the experiment up to hundreds of megahertz. A digital pulse pattern generator with an insufficient sampling rate cannot properly trigger the laser pulses and provide a start click for the measurement to the TDC.

• Low precision above the range of the other components: The aforementioned low timing jitter required for the detector and TDC also applies to the pulse pattern generation, triggering the measurement. Hence, the digital pulses must have timing precision on the order of the detector’s and TDC’s timing jitter.

Swabian Instruments are well-suited from a signal acquisition and signal generation perspective to satisfy the demands of Quantum Dot (QD) characterization experiments.

On the one side, Time Taggers are well-suited for signal acquisition and analysis within QD experiments since they offer an advanced time-to-digital converter (TDC) instrument with:

• Picosecond-level timing precision: Swabian Instruments’ Time Taggers provide a 1 ps digital resolution and down to 1.5 ps timing jitter (RMS) of the TDCs. Thus, they are well-suited for the sub-nanosecond fast emission dynamics of QDs.

• High input frequencies and data transfer rates: High brightness and fast pump laser repetition rates lead to several Mcounts/s photon emission rates, which the detector and timing electronics system must handle. The Time Tagger Ultra and Time Tagger X can process up to 475 and 700 Mcounts/s incoming event rates, respectively. The sum of all of the measured time tags is then transferred at a rate of up to 90 Mtags/s via USB3.0 to the computer. For higher demands, the Time Tagger X allows for an FPGA link approach to stream data to a secondary FPGA via SFP or QSFP+ interface, achieving 300 and 1200 MTags/s transfer rates, respectively.

• Versatile time tag processing: Swabian Instruments’ Time Taggers stream the time tags with minimal onboard pre-processing to the data acquisition computer. This architecture permits multiple independent measurements using the same time tags. The powerful API and Time Tagger Lab GUI provide an easy-to-use user interface with predefined measurement classes such as Countrate, Histogram, Correlation, and Coincidences, well-suited for QD characterization.

On the other side, the Pulse Streamer 8/2 offers an easy yet powerful system for digital pulse pattern generation, advantageous for QD characterization, given its:

• High sampling rate: the 1 GHz sampling rate of the Pulse Streamer 8/2 allows for arranging the digital pulse patterns on a 1 ns grid and a high trigger repetition rate of up to 125 MHz.

• Low timing jitter: The rising and falling edges of the pulses generated by the Pulse Streamer 8/2 show a timing jitter below 50 ps, which allows for a precise triggering of the laser pulses and the measurements performed by the Time Tagger.

Literature work in which Swabian Instruments Time Taggers have been demonstrated for Quantum Dots includes Prof. Peter Lodahl’s work titled Entangling a hole spin with a time-bin photon: a waveguide approach for quantum dot sources of multi-photon entanglement ⁷ and Prof. Peter Michler’s work on Controllable Delay and Polarization Routing of Single Photons ⁸. Lodahl’s group at the University of Cambridge leverages Swabian Instruments’ Time Tagger Ultra and is focused on integrating QD with photonic waveguides to offer reliable sources of single photons for quantum computing and Quantum Key Distribution (QKD).

Michler’s group at the University of Stuttgart leverages Swabian Instruments’ Time Tagger 20 to evaluate photon statistics from single-photon detection experiments from a semiconductor QD as they seek to improve quantum implementations via on-chip quantum photonics. Some of his latest projects explore bright Purcell-enhanced single-photon sources in telecom O-band (based on QDs in circular Bragg gratings)⁹, resonance fluorescence of single In(Ga)As QDs emitting in telecom C-band ¹⁰, and an efficient and stable fiber-to-chip coupling to inject single photons from telecom QD into a silicon-on-insulator ¹¹.

The recent developments in the field of photon number resolution (PNR), which Swabian Instruments is pushing (see Photon Number Resolution (PNR)), could permit reducing the effort in characterizing the QD emission in terms of brightness, indistinguishability, and purity.

So far, different optical setups are needed to measure these figures of merit as described in the previous section. However, if the two SPDs in combination with the ultra-high timing precision of the Time Tagger X have the capability of resolving photon numbers of one, two, and three or more photons, only the HOM interference setup (Fig. 3b) is needed to measure all relevant parameters of the QD simultaneously. In such a setup, while performing a HOM interference experiment, the count rate or brightness can be deduced from the time tags and photon number on each detector.

The purity can also be evaluated from the same time tag stream. It can be verified that no coincidences between both detectors have been measured simultaneously $(\tau=0)$ and events where just one, three, or more photons have impinged on the detector can be discarded to only count the two photon events ($g^{(2)} (\tau)$ correlation). Last but not least, the indistinguishability is accessible by filtering the events with respect to a two-photon event on either detector channel, where no coincidence with a click on the other detector was measured (HOM-interference).

To summarize, the high timing precision in the single-digit picosecond regime, combined with the high data acquisition rates, makes the Swabian Instruments’ Time Tagger an ideal solution for performing QD characterisation measurements. Further, the Pulse Streamer 8/2 provides a comprehensive solution for orchestrating such an experiment by controlling the different devices involved through digital pulse patterns.

Quantum Dot Single-Photon Source Characterization Using High-Precision Timing Electronics | Swabian Instruments Time Tagger & Pulse Streamer

Swabian Instruments’ Time Tagger and Pulse Streamer provide picosecond-level timing resolution, fast digital pulse generation, and high data-throughput capabilities used in the characterization of quantum-dot single-photon sources.

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Time-Resolved Photoluminescence (TRPL)

Time-resolved photoluminescence (TRPL) is a powerful technique that measures the photoluminescence decay (emission lifetime) of materials after pulsed excitation, thereby probing their optical and electronic properties. By tracking how excited states relax back to the ground state, TRPL distinguishes between radiative and non-radiative pathways, yielding lifetimes that report on charge-carrier dynamics, trap/defect activity, and other loss mechanisms.

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