Dynamical modeling of pulsed two-photon interference

Fischer, Kevin A.; Müller, Kai; Lagoudakis, Konstantinos G.; Vučković, Jelena

doi:10.1088/1367-2630/18/11/113053

Cited by 61 publications

(124 citation statements)

References 40 publications

(133 reference statements)

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“…[]):

\begin{matrix} true \\ right \overset{H}{true} (t) = \overset{H}{true} + [{normalΩ}^{*} false(t false) \hat{σ} + Ω false(t false) {\overset{σ}{true}}^{†}] \end{matrix}

where

Ω (t)

is the “driving pulse” given by

\begin{matrix} true \\ right normalΩ (t) = g^{*} (ω_{E}) \int_{- \infty}^{\infty} α (ω) \exp (- i ω t) normald ω \end{matrix}

This driving term is similar to that obtained in a treatment of light–matter interaction in which the optical fields are treated classically. Addition of this driving term to the Hamiltonian allows us to solve a problem in which the loss channel is initially in the vacuum state—such a problem can be numerically analyzed within the master‐equation framework or the scattering matrix framework …”

Section: Fundamentalsmentioning

confidence: 99%

“…A very popular experimental metric for characterizing states emitted from single‐photon sources is the two‐time second‐order correlation function

g^{(2)} false(t_{1}, t_{2} false)

, which is a measure of the joint probability of detecting a photon at both the time instants t 1 and t 2 . Mathematically, assuming that the detector is located at

x = L

, this is defined by (note that all the operators are the position annihilation operators):

\begin{matrix} true \\ left g^{false(2 false)} (t_{1}, t_{2}) = \frac{(〈|, Ψ) {\hat{a}}^{†} (t_{1}; L) {\hat{a}}^{†} (t_{2}; L) \overset{a}{true} (t_{2}; L) \overset{a}{true} (t_{1}; L) (|〉, Ψ)}{(〈|, Ψ) {\hat{a}}^{†} (t_{1}; L) \overset{a}{true} (t_{1}; L) (|〉, Ψ) (〈|, Ψ) {\hat{a}}^{†} (t_{2}; L) \overset{a}{true} (t_{2}; L) (|〉, Ψ)} \\ left = (〈|, Ψ) {\hat{a}}^{†} (L - v_{G} t_{1}) {\hat{a}}^{†} (L - v_{G} t_{2}) \overset{a}{true} (L - v_{G} t_{2}) \overset{a}{true} (L - v_{G} t_{1}) (|〉) \end{matrix}

…”

Section: Fundamentalsmentioning

confidence: 99%

“…In a realistic experimental setting, however, the photodetector usually has a response time which is much larger than the temporal width of the light being emitted from the light source. This practical limitation prohibits the exact measurement of

g^{(2)} false(t_{1}, t_{2} false)

as a function of

(t_{1}, t_{2})

, rather it allows the measurement of the integrated two‐time correlation g (2) [0]:

\begin{matrix} true \\ right g^{false(2 false)} [0] = \frac{\int \int (〈|, Ψ) {\hat{a}}^{†} (t_{1}; L) {\hat{a}}^{†} (t_{2}; L) \overset{a}{true} (t_{2}; L) \overset{a}{true} (t_{1}; L) (|〉, Ψ) normald t_{1} normald t_{2}}{{[\int 〈normalΨ| {\overset{a}{true}}^{†} false(t; L false) \hat{a} false(t; L false) |normalΨ〉 d t]}^{2}} \end{matrix}

Even if a precise measurement of

g^{(2)} false(t_{1}, t_{2} false)

as a function of t 1 and t 2 was possible, g (2) [0] provides information about the two‐photon statistics of the entire photon pulse. Both

g^{(2)} false(t_{1}, t_{2} false)

and g (2) [0] have remarkably different values for different states of light, making it a suitable tool for characterizing the state of light emitted by a light source.…”

Section: Fundamentalsmentioning

confidence: 99%

“…This dead time is often larger than the pulsewidth of the light emitted by the photon source, thereby making it impossible to measure the two‐time correlation with just one detector. An alternative scheme to get around this issue is the Hanbury–Brown and Twiss interferometer (HBT)—this scheme ( Figure 3a) splits the light emitted by the source into two waveguides via a 50–50 beam splitter (

θ = π / 4

), and then performs photodetection in the two waveguides separately . The phase shift φ shown in the setup models random variation in the path lengths of the two arms of the interferometer due to environmental fluctations—the result of an experimental measurement performed over repeated trial effectively averages over this phase shift.…”

Section: Fundamentalsmentioning

confidence: 99%

“…In both cases, the beam splitter is assumed to be a 50–50 beam splitter (

θ = π / 4

) and the phase shift ϕ models random variations between the path lengths of the two branches of the interferometer. Adapted under the terms of the Creative Commons Attribution 3.0 license . Copyright 2016, The Authors, Published by IOP Publishing Ltd on behalf of Deutsche Physikalische Gesellschaft.…”

Section: Fundamentalsmentioning

confidence: 99%

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Generation of Non‐Classical Light Using Semiconductor Quantum Dots

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Sources of non‐classical light are of paramount importance for future applications in quantum science and technology such as quantum communication, quantum computation and simulation, quantum sensing, and quantum metrology. This Review is focused on the fundamentals and recent progress in the generation of single photons, entangled photon pairs, and photonic cluster states using semiconductor quantum dots. Specific fundamentals which are discussed are a detailed quantum description of light, properties of semiconductor quantum dots, and light–matter interactions. This includes a framework for the dynamic modeling of non‐classical light generation and two‐photon interference. Recent progress is discussed in the generation of non‐classical light for off‐chip applications as well as implementations for scalable on‐chip integration.

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“…[]):

\begin{matrix} true \\ right \overset{H}{true} (t) = \overset{H}{true} + [{normalΩ}^{*} false(t false) \hat{σ} + Ω false(t false) {\overset{σ}{true}}^{†}] \end{matrix}

where

Ω (t)

is the “driving pulse” given by

\begin{matrix} true \\ right normalΩ (t) = g^{*} (ω_{E}) \int_{- \infty}^{\infty} α (ω) \exp (- i ω t) normald ω \end{matrix}

Section: Fundamentalsmentioning

confidence: 99%

“…A very popular experimental metric for characterizing states emitted from single‐photon sources is the two‐time second‐order correlation function

g^{(2)} false(t_{1}, t_{2} false)

, which is a measure of the joint probability of detecting a photon at both the time instants t 1 and t 2 . Mathematically, assuming that the detector is located at

x = L

, this is defined by (note that all the operators are the position annihilation operators):

\begin{matrix} true \\ left g^{false(2 false)} (t_{1}, t_{2}) = \frac{(〈|, Ψ) {\hat{a}}^{†} (t_{1}; L) {\hat{a}}^{†} (t_{2}; L) \overset{a}{true} (t_{2}; L) \overset{a}{true} (t_{1}; L) (|〉, Ψ)}{(〈|, Ψ) {\hat{a}}^{†} (t_{1}; L) \overset{a}{true} (t_{1}; L) (|〉, Ψ) (〈|, Ψ) {\hat{a}}^{†} (t_{2}; L) \overset{a}{true} (t_{2}; L) (|〉, Ψ)} \\ left = (〈|, Ψ) {\hat{a}}^{†} (L - v_{G} t_{1}) {\hat{a}}^{†} (L - v_{G} t_{2}) \overset{a}{true} (L - v_{G} t_{2}) \overset{a}{true} (L - v_{G} t_{1}) (|〉) \end{matrix}

…”

Section: Fundamentalsmentioning

confidence: 99%

g^{(2)} false(t_{1}, t_{2} false)

as a function of

(t_{1}, t_{2})

, rather it allows the measurement of the integrated two‐time correlation g (2) [0]:

\begin{matrix} true \\ right g^{false(2 false)} [0] = \frac{\int \int (〈|, Ψ) {\hat{a}}^{†} (t_{1}; L) {\hat{a}}^{†} (t_{2}; L) \overset{a}{true} (t_{2}; L) \overset{a}{true} (t_{1}; L) (|〉, Ψ) normald t_{1} normald t_{2}}{{[\int 〈normalΨ| {\overset{a}{true}}^{†} false(t; L false) \hat{a} false(t; L false) |normalΨ〉 d t]}^{2}} \end{matrix}

Even if a precise measurement of

g^{(2)} false(t_{1}, t_{2} false)

as a function of t 1 and t 2 was possible, g (2) [0] provides information about the two‐photon statistics of the entire photon pulse. Both

g^{(2)} false(t_{1}, t_{2} false)

and g (2) [0] have remarkably different values for different states of light, making it a suitable tool for characterizing the state of light emitted by a light source.…”

Section: Fundamentalsmentioning

confidence: 99%

θ = π / 4

Section: Fundamentalsmentioning

confidence: 99%

“…In both cases, the beam splitter is assumed to be a 50–50 beam splitter (

θ = π / 4

Section: Fundamentalsmentioning

confidence: 99%

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Quantum mechanics promises to have a strong impact on many aspects of research and technology, improving classical analogues via purely quantum effects. A large variety of tasks are currently under investigation, for example, the implementation of quantum computing, sensing, metrology, and communication. From a general perspective, in a similar way as classical computing benefited by the reduction of the device footprint, enabling the realization of highly complex chips, a range of quantum applications will sensibly improve thanks to the successful realization of on-chip quantum photonics. Conversely to bulky table-top experiments, it would be very advantageous to transfer all required functionalities on the same quantum photonic chip. The key elements for quantum photonic circuits are on-demand nonclassical light sources, a versatile photonic logic, the ability to store quantum information, and highly efficient detectors, directly integrated on-chip. Among several systems capable of the efficient generation of singleand indistinguishable photons, quantum dots are rapidly establishing as one of the most appealing candidates. This paper reviews the recent progress in the on-chip integration of quantum-dot-based nonclassical light sources as well as in the development of the main building blocks, either integrated monolithically or hybridly on a compact and scalable platform. IntroductionFrom the foundation of quantum mechanics in the early 20th century to explain fundamental physical observations, over the development of transistors and lasers in the 1950s and 1960s, the second quantum revolution is now in full swing. The driving force behind this continuing "quantum footrace" are quantum mechanical effects based on superposition and entanglement that can lead to profound changes. Especially in the field of quantum information science, dramatic improvements are expected in terms of increased computational speed and communication security if compared with classical counterparts.Talking about quantum supremacy, two problems-Grover's algorithm for the efficient search in large unsorted databases and Shor's algorithm for the prime factorization of large integers-are frequently mentioned. [1][2][3] Grover's quantum search algorithm can find an element of a search space M in O( √ M) operations compared to the best known classical algorithms approximately requiring O(M) steps. [4] Shor's algorithm can prime factorize large integers with N bits in polynomial speed compared to the exponential scaling of classical algorithms. Currently, several cryptography schemes in electronic communication systems rely on the difficulty of prime factorization as its security method. Consequently, a quantum computer could break the cryptographic keys quickly by calculating or searching exhaustively all key possibilities, which may allow an eavesdropper to intercept the communication channel. [5] However, quantum key distribution schemes can be alternatively used, which are based on the secure exchange of a cryptographic key between remote...

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Deterministic nanoassembly may enable unique integrated on-chip quantum photonic devices. Such integration requires a careful large-scale selection of nanoscale building blocks such as solid-state single-photon emitters by means of optical characterization. Second-order autocorrelation is a cornerstone measurement that is particularly time-consuming to realize on a large scale. Supervised machine learning-based classification of quantum emitters as "single" or "not-single" is implemented based on their sparse autocorrelation data. The method yields a classification accuracy of 95% within an integration time of less than a second, realizing roughly a 100-fold speedup compared to the conventional Levenberg-Marquardt fitting approach. It is anticipated that machine learning-based classification will provide a unique route to enable rapid and scalable assembly of quantum nanophotonic devices.

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Dynamical modeling of pulsed two-photon interference

Cited by 61 publications

References 40 publications

Generation of Non‐Classical Light Using Semiconductor Quantum Dots

Generation of Non‐Classical Light Using Semiconductor Quantum Dots

Semiconductor Quantum Dots for Integrated Quantum Photonics

Rapid Classification of Quantum Sources Enabled by Machine Learning

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