Complex frequency-dependent quadrature squeezing in semiconductor lasers

arXiv:2606.26266 · quant-ph, cond-mat.mes-hall, physics.optics · Submitted 2026-06-24 · Read on arXiv

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Introduction to the show: ident: Quantum Radio. Generated commentary on the latest quantum physics and condensed matter papers.

Kai: Today's paper: "Complex frequency-dependent quadrature squeezing in semiconductor lasers".

Mira: The gist: This work presents a comprehensive study of quadrature squeezing in a quantum well laser using a fully quantum Langevin approach,

Kai: First, who's behind it and why it matters.

Title and authors: Mira: So we're starting with the title and authors for this paper, "Complex frequency-dependent quadrature squeezing in semiconductor lasers." It immediately tells us they are focusing on how squeezing changes depending on the frequency of light you look at.

Kai: And the authors are Daniele Nello Laboratoire PhLAM from France and Lorenzo Columbo from Politecnico di Torino, Italy. They’re bringing together expertise from different groups to tackle this complex noise problem.

Lev: It sounds like they're setting up a solid foundation by using the quantum mechanical model for the quantum-well laser that was introduced in reference thirteen which justifies these stochastic rate equations they are using for the laser dynamics <ref:2606.26266#pg2,the quantum mechanical model for the quantum-well laser>.

Kai: Right. They are taking that microscopic model and turning it into a macroscopic system of Langevin equations to see how things evolve when you look at noise variations like delta X, delta Y, and the number of electronhole pairs N.

The paper's summary: Mira: What they summarize is that they compute the covariance matrix analytically, which lets them characterize the output quadratures' spectra completely. They are identifying specific optimal squeezing curves by plotting this generalized output quadrature variation Q(theta)Ropt,out with its variance V (theta, omega).

Kai: It’s not just showing a simple line of squeezing; they are mapping out these squeezing maps for different values of theta to see the whole picture of how the noise behaves across frequencies.

Lev: They point out that in the quiet pumping regime, where you have negligible electronic pumping noise, and also when you pump at sufficiently high currents, they can find a region of squeezing at low frequencies around theta equals zero.

Mira: And they also note that there’s a pole at omega equals zero for the Y quadrature component when theta is pi over two; that tells us something specific about the system's behavior at those different points.

The paper's improvements: Kai: Now, looking at what this paper suggests improves things, it highlights that they are able to get frequency-dependent squeezing and complex or hidden squeezing for the first time in this type of laser.

Mira: That complex or hidden squeezing is particularly interesting because the spectral covariance matrix contains information that standard homodyne detection just can't access directly. It’s encoded in its imaginary part, which relates correlations between optical sidebands.

Lev: From a practical standpoint, this means we need new measurement schemes because you can’t just rely on the basic amplitude and phase measurements anymore to find the best noise reduction point.

Kai: And they propose synodyne detection as a scheme specifically designed to access that complex part of the covariance matrix. This allows you to measure variances like V (theta, phi, omega) which includes terms for the real and imaginary parts of CovXY (omega).

Conclusion: Mira: So to wrap up, this paper shows that optimal noise reduction can happen along quadratures that aren't directly accessible through standard homodyne detection. That hidden squeezing means we can lower the noise in the global minimum of squeezing.

Kai: And because of this hidden squeezing, it becomes a resource for quantum sensing and metrology that we might not have seen before. It’s about leveraging information that is normally invisible to us with simple tools.

Lev: I think the main thing they establish is how the linewidth enhancement factor, or alpha-factor, really governs the coupling between the carrier dynamics, intensity, and phase of the field. That factor seems like a key differentiator between semiconductor lasers and things like atomic or gas lasers.

Mira: Indeed. The alpha-factor shifts where you find the maximum relaxation oscillations on that theta axis, which changes how that optimal squeezing curve looks overall. They show this dependence is crucial for understanding the system's behavior under different driving conditions.

Kai: So we’re looking at a comprehensive study of "Complex frequency-dependent quadrature squeezing in semiconductor lasers." It confirms that these systems are platforms for generating non-classical light with features that go beyond simple amplitude noise.

Lev: We have seen how this information is encoded in those complex correlations, and it gives us a path forward for better quantum measurements.

Laboratoire PhLAM (UMR 8523), Universit´e de Lille · Dipartimento di Elettronica e Telecomunicazioni, Politecnico di Torino

quant-ph, cond-mat.mes-hall, physics.optics

Submitted: 2026-06-24

Updated: 2026-10-08

Comments: 11 pages, 5 figures

License: http://creativecommons.org/licenses/by/4.0/

Importance score: 73/100

The gist: The gist: This work presents a comprehensive study of quadrature squeezing in a quantum well laser using a fully quantum Langevin approach, revealing both frequency-dependent squeezing and complex or

Key concepts

Quadrature Squeezing
This refers to reducing the noise in specific measurable properties of light, like amplitude or phase fluctuations. In this laser study, the researchers found that the best way to reduce noise (the 'squeezed' quadrature) changes depending on the frequency of the light being emitted.
Frequency Dependence
The paper shows that which quadrature is most useful for squeezing is not constant; it rotates as you change the frequency. This means a noise reduction technique optimized for one part of the laser's output works best at a different frequency than another, extending the useful noise reduction range.
Hidden/Complex Squeezing
This is a type of squeezing that cannot be seen using typical measurement techniques like standard homodyne detection. It exists in the imaginary part of the system's covariance matrix and represents correlations between different optical sidebands, offering a resource for quantum applications that are otherwise invisible.

Terminology

Summary

The gist: This work presents a comprehensive study of quadrature squeezing in a quantum well laser using a fully quantum Langevin approach, revealing both frequency-dependent squeezing and complex or hidden squeezing features for the first time in this context.

Theoretical Framework

The analysis is based on developing a general framework that goes beyond the amplitude quadrature and gives access to the full quadrature noise structure of the emitted field <ref:2606.26266#pg2> The analysis is based on a microscopic model of a quantum well active material and retains the full dynamics of the active medium, avoiding adiabatic elimination <ref:2606.26266#pg2> The system of macroscopic quantum Langevin equations for the creation/annihilation operator of the photon field inside the laser cavity A and the number of electronhole pairs in the quantum well N reads (1) <ref:2606.26266#pg2> This system is linearized around the semiclassical CW stationary solution <ref:2606.26266#pg2> The linear system of equations for the quadratures variation δX, δY, δN with respect to stationary values is given by (4) <ref:2606.26266#pg2>

Key Physical Phenomena

The study highlights several key features emerging from the full quadrature description <ref:2606.26266#pg2>

  1. Frequency dependence of squeezing: The optimal squeezing quadrature rotates at higher frequencies, extending the sub-shot-noise bandwidth beyond that predicted by amplitude squeezing alone <ref:2606.26266#pg2>

  2. Role of the linewidth enhancement factor (α-factor): The αH factor is essential for the emergence of frequency-dependent squeezing and hidden squeezing <ref:2606.26266#pg2> It determines a shift of the relaxation oscillations maximum on the θ axis, changing in turn the shape of the optimal squeezing curve <ref:2606.26266#pg2>

  3. Hidden/Complex Squeezing: The spectral covariance matrix contains information inaccessible to standard homodyne detection, and its imaginary part encodes correlations between optical sidebands, giving rise to the so-called hidden [20–23] or complex [24] squeezing <ref:2606.26266#pg2>

Measurement and Detection Schemes

The complete output covariance matrix of the optical output is given by (11) <ref:2606.26266#pg2> The generalized output quadrature variations are identified by Q(θ)Ropt,out, with its associated variance V (θ, ω) defined as (13) <ref:2606.26266#pg2> Synodyne detection is proposed as a scheme to access the complex part of the covariance matrix <ref:2606.26266#pg2> This scheme allows access to the complex part because V (θ, ϕ, ω) = cos(θ) 2 δX(ω) 2 + sin(θ) 2 δY (ω) 2 + 2 cos(ϕ) sin(θ) cos(θ)Re(CovXY (ω)) + 2 sin(ϕ) sin(θ) cos(θ)Im(CovXY (ω)) <ref:2606.26266#pg2> The resulting variance Vmin (ω), obtained using the Rayleigh-Ritz variational principle, highlights a further contribution of squeezing in the global minimum at ω = 0, due to the presence of hidden squeezing <ref:2606.26266#pg2>

Conclusions and Outlook

The full quadrature description reveals that optimal noise reduction may occur along quadratures that are not directly accessible through standard homodyne detection <ref:2606.26266#pg2> Taking into account this hidden squeezing renders possible to lower the amount of noise in the global minimum of squeezing <ref:2606.26266#pg2> Hidden squeezing represents a potentially exploitable resource for quantum sensing and metrology <ref:2606.26266#pg2> The αH factor governs the coupling between the carrier dynamics, the intensity and the phase of the field, which is a key feature differentiating semiconductor lasers from atomic/gas lasers <ref:2606.26266#pg2> Future work can extend this analysis to other types of semiconductor lasers such as quantum dots and QCLs <ref:2606.26266#pg2> Generalizing the analysis to a multimodal system, such as studying quantum correlations between different lines of a spontaneously generated comb, is another important direction for research <ref:2606.26266#pg2>

Appendix Details

The noise terms in the linearized equations are decomposed into Ncar, NP and Nopt <ref:2606.26266#pg2> The scalar σcar is the noise associated to the carrier’s number <ref:2606.26266#pg2> The cross-correlation term between the carriers and the field noise is given by (C8)

Figure Interpretation

The squeezing maps, such as Fig. 1, highlight how the region of squeezing appears at a = 4 and becomes more visible for higher values of the currents The shift of the relaxation oscillations with the current is well known in the literature The role of αH, while not changing the entity of the amplitude squeezing, is to modify the shape of the optimal squeezing curves (Eq. 15) and its asymptotic value zopt The region of squeezing appears at a = 4 and is subsequently enlarged for higher values of the currents The peak of relaxation oscillations is shifted in frequency with the current, a fact well known in the literature [15]

References Cited

[1] R. Schnabel, Squeezed states of light and their applications in laser interferometers, Physics Reports 684, 1 (2017)

[3] E. Oelker, R. E. S. Polzik, J. Abadie, et al., Frequencydependent squeezing for advanced ligo, Physical Review Letters 116, 041102 (2016)

[4] M. A. Taylor, J. Janousek, V. Daria, J. Knittel, B. Hage, H.-A Bachor, and W. P Bowen, Biological measurement beyond the quantum noise limit using squeezed light, Nature Photonics 7, 229 (2013)

[5] M. Genovese, Real applications of quantum metrology, Journal of Optics 18, 073002 (2016)

[9] S. Machida and Y. Yamamoto, Observation of subpoissonian photon statistics in a semiconductor laser, Physical Review Letters 60, 792 (1988)

[13] W. W Chow, S. W Koch, and M. S III, SemiconductorLaser Physics (Springer-Verlag, Berlin, Heidelberg, 1994)

[14] Y. Yamamoto, S Machida, and O Nilsson, Amplitude squeezing in a pump-noise-suppressed laser oscillator, Physical Review A 34, 4025 (1986)

[15] L. A Coldren, S. W Corzine, and M L Maˇsanovi´c, Diode Lasers and Photonic Integrated Circuits, 2nd ed. (Wiley, 2012)

[19] C H Henry, Theory of the linewidth of semiconductor lasers, IEEE Journal of Quantum Electronics 18, 259 (1982)

[30] M J Collett, R Loudon, and C W Gardiner, Quantum theory of optical homodyne and heterodyne detection, Journal of Modern Optics 34, 881 (1987)

[31] R A Horn and C R Johnson, Matrix Analysis, 2nd ed.

Improvements for AI systems

  1. Confidence in non-classical light generation for integrated quantum devices: The AI system can predict the emergence of frequency-dependent squeezing and complex or hidden squeezing in a semiconductor laser by analyzing the spectral covariance matrix and its imaginary part, which is encoded [in the imaginary part] as correlations between optical sidebands, giving rise to the so-called hidden [or complex] squeezing.

  2. Quantum sensing protocol optimization: The AI can devise measurement strategies beyond standard homodyne detection by employing schemes like synodyne detection or resonator detection, specifically using a generalized quadrature variation such as V (θ, ϕ, ω) = Q(θ, ϕ) Σopt,out(ω) Q T (θ, ϕ), to access the smallest of which is the frequency-dependent minimum of noise.

  3. Parameter-dependent resource allocation: The AI can dynamically adjust measurement parameters based on the Henry linewidth enhancement factor (αH), as it reveals that the αH factor rotates the optimal squeezing curve and modifies the squeezing map, without changing the amplitude squeezing spectrum.

  4. Threshold identification for quantum advantage: The system can precisely identify what is the threshold is for amplitude squeezing to appear by analyzing how the amount of noise at this point does not surpass 5 dB compared to the global minimum attainable by leveraging hidden squeezing across varying pumping currents.

Abstract

We present a comprehensive study of quadrature squeezing in a quantum well laser based on a fully quantum Langevin approach. We compute the frequency-resolved squeezing map of the laser field and identify optimal squeezing curves, revealing, for the first time to our knowledge, both frequency-dependent squeezing and complex or hidden squeezing in a semiconductor laser. We further analyse the role of the linewidth enhancement factor (alpha-factor) in the emergence of these features. Our results establish semiconductor lasers as a platform for the generation of non-classical light and open new perspectives for their application in quantum communication and sensing.

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