Memory effects in pulsed optomechanical systems

Ariel Norambuena; Bing He; Hachisko Tapia-Maureira; Massimiliano Di Ventra

REVIEW 3 major objections 5 minor 51 references

Memory effects in pulsed optomechanical systems

T0 review · 3 major / 5 minor · reviewed 2026-08-07 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

Pith's one-line read A pulsed laser drive can turn a cavity optomechanical system into a programmable quantum memory element, with the pulse shape — Gaussian, sinusoidal, or square-sinusoidal — selecting the regime, up to a form factor of 0.965.

desk verdict A credible semiclassical demonstration of pulse-tuned hysteresis memory in optomechanics; the quantum-certified part is still missing. read the letter →

arxiv 2506.03455 v1 pith:Q7MIUOGY submitted 2025-06-03 quant-ph nlin.CD

Hachisko Tapia-Maureira , Bing He , Massimiliano Di Ventra , Ariel Norambuena This is my paper

classification quant-phnlin.CD

keywords optomechanicsquantummemorydynamicalhysteresismemristivesystemspulsedlaserdrivingmean-fielddynamicsformfactorphononamplitudelocking

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

Cavity optomechanical systems — optical resonators whose movable mirror couples light to a mechanical oscillator — can act as programmable quantum memory elements when driven by pulsed laser light. The authors show that the pump history leaves a trace in the photonic and phononic observables, appearing as hysteresis loops in the plane of input $E(t)$ versus output, with Gaussian trains, sinusoidal, and square-sinusoidal drives producing distinct loop structures: single-, double-, and multi-loop hysteresis, an adiabatic collapse to a memoryless response, and energy-storing versus energy non-storing regimes. The memory content of a loop is measured by the dimensionless form factor $F = 4\pi A/P^2$ (enclosed area over perimeter squared), and a genetic-algorithm search over drive parameters pushes it to $F = 0.965$ for square-sinusoidal driving, above the values the same metric gives for existing photonic and polaritonic quantum memristors. If the claim holds, this gives a mature experimental platform a tunable, history-dependent response relevant to neuromorphic and quantum information processing, without any engineered environment or feedback.

What carries the argument

The load-bearing object is the four-dimensional mean-field system for the optical and mechanical quadratures $(X_c, P_c, X_m, P_m)$, Eqs. (15)–(18), obtained by replacing operator products with products of expectation values in the Heisenberg equations of the radiation-pressure Hamiltonian. The nonlinear radiation-pressure term $\sqrt{2}\,g_m X_m X_c$ couples the mechanical displacement to the cavity photon number and is the source of history dependence, while the cavity damping $\kappa$ and mechanical damping $\gamma_m = \omega_m/Q$ convert each past instant of the drive into an exponentially fading contribution to the present; the paper's own appendix shows the enclosed area vanishes when $\kappa = 0$, so dissipation is what makes the memory readable. The metric that carries the quantitative claims is the dimensionless form factor $F = 4\pi A/P^2$ of the input–output loop, with area $A$ computed by Green's theorem and perimeter $P$ by arc length; by the isoperimetric inequality $0 \le F \le 1$, so $F$ measures how close a loop comes to the ideal circular hysteresis that maximally encodes memory.

What would settle it

Two checks would settle the central claim. Numerically: run a full quantum master-equation or truncated-Wigner calculation at reduced photon numbers where exact simulation is feasible and compare the input–output loops and optimized form factors with the mean-field predictions; material deviations would show the memory metric is a semiclassical artifact. Experimentally: drive a Fabry–Pérot or microtoroidal optomechanical cavity with the square-sinusoidal pulse $E(t) = E_0\sin^2(\omega t)$ at the reported optimum ($E_0 \approx 7.5\times10^{5}\kappa$, $\omega \approx 1.64\kappa$) and measure the loop of $\langle a^\dagger a\rangle$ versus $E(t)$; a form factor far below 0.965, or no closed loop at all, would falsify the quantitative claim.

Watch

Extended reading notes

Core claim

On its own terms, the paper claims that memory — the dependence of a system's present state on its past driving — arises naturally from the intrinsic nonlinear dynamics of a dissipative optomechanical cavity, and that the memory's character and strength can be programmed by shaping the laser pulse. Starting from the Hamiltonian $H = \Delta a^\dagger a + \omega_m b^\dagger b - g_m a^\dagger a(b^\dagger + b) + iE(t)(a^\dagger - a)$ and a mean-field decoupling of the Heisenberg equations, the authors derive response-kernel expressions in which the mean photon and phonon numbers at time $t$ convolve earlier values of the drive with decaying exponentials $e^{-2\kappa|t-t'|}$ and $e^{-2\gamma_m|t-t'|}$, making time non-locality explicit. Under periodic driving, plots of $\langle a^\dagger a\rangle$ or $\langle b^\dagger b\rangle$ against $E(t)$ close into loops; a nonzero enclosed area signals memory, loops through the origin signal an energy non-storing response, and loops that avoid the origin signal energy storage. The quantitative discovery is that optimized pulse shapes yield $F_\mathrm{opt} = 0.965$ for photons and $0.963$ for phonons under square-sinusoidal driving, with Gaussian trains reaching $0.925$ and $0.863$, and that strong Gaussian pumping produces discrete dynamical jumps in the phonon number reminiscent of amplitude locking.

Load-bearing premise

Everything quantitative in the paper rests on a mean-field (semiclassical) approximation in which quantum fluctuations and correlations between the optical and mechanical modes are neglected, an approximation the authors take as well established for strong driving but justify by a single cited work; if those correlations are significant at the parameters used ($g_m = 10^{-5}\kappa$, $Q = 10^4$, photon numbers up to about $10^{11}$), the hysteresis loops, form factors, and phonon jumps could be semiclassical artifacts.

Editorial extensions

If this is right

Pulse shaping alone selects the memory regime in a single device: narrow Gaussian pulses give energy non-storing single- or multi-loop hysteresis, slow wide pulses collapse the loop to a memoryless response, and square-sinusoidal pulses give energy-storing loops whose output persists after the field vanishes.
The optimized form factors imply that an optomechanical cavity driven this way encodes more memory per cycle than the photonic ($F \approx 0.58$) and polaritonic ($F \approx 0.19$) quantum memristors benchmarked in the paper on the same metric.
Memory duration is set by the cavity decay time: the Dirac-delta analysis gives a response that decays as $e^{-2\kappa(t-t_s)}$, so the same device's memory lifetime can be tuned by cavity design without changing the protocol.
Because the form factor is a purely geometric quantity, the optimization protocol transfers to any driven-dissipative platform whose input–output trajectories close into loops, giving a common benchmark for trapped ions, superconducting circuits, and photonic devices.
The energy-storing regime, where the photon momentum stays near its maximum while the input vanishes, suggests the device can act as a short-term optical buffer whose stored excitation persists between pulses.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

Beyond the paper: the reported form-factor values come from mean-field dynamics with photon numbers up to about $10^{11}$; a full quantum treatment would likely smear the sharp phonon jumps and could shift the optimized $F$ values, so the true quantum bound on memory efficiency remains an open question.
Beyond the paper: the time-non-locality formalism invites an information-theoretic reading the authors do not give — since the loop area bounds how many distinct input histories a cycle can distinguish, $F$ could serve as a proxy for per-cycle memory capacity in bits.
Beyond the paper: in the energy-storing regime the mechanical oscillator keeps excitation between pulses, so a natural experiment is to measure the input–output loop area as a function of a dark interval inserted between pulses, directly mapping the memory kernel $e^{-2\kappa|t-t'|}$ the theory predicts.
Beyond the paper: the multi-loop and n-loop hysteresis regimes could be read as a physical reservoir — feeding a temporal bit sequence through the drive and classifying the photonic output trajectories would test whether the device's history dependence is rich enough for neuromorphic computing.

Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

I read through arXiv:2506.03455. The genuinely new thing is a proposal, backed by numerical simulation, that a pulsed coherent drive can produce and tune hysteresis loops in the photon and phonon numbers of a cavity optomechanical system. The response-kernel structure (Eqs. 9-10) is actually exact: the optomechanical coupling cancels in the time-derivative of a†a and b†b, so the convolution forms follow from the Heisenberg equations without approximation. That part is solid. The mean-field factorisation is the only real approximation, and the paper's qualitative story—fast pulses give loops, slow pulses do not; some drives store energy, others do not—is credible.

Credit where due: the input-output framework is clearly explained, the form-factor metric is a reasonable dimensionless benchmark, and the numerical exploration covers three drive families with consistent results. The open comparison with other platforms is a useful service to the community.

The soft spots are real. Most important: the mean-field approximation is never checked. In the optimized regime the effective coupling G = gm sqrt(⟨a†a⟩) is about 3κ while the mechanical damping γm = ωm/Q ≈ 2×10^-3 κ, so the cooperativity is ~10^4. That is a strongly coupled, underdamped regime where quantum correlations can feed back into the very observables that define the loops. The 'dynamical quantized jumps' in Sec VI E are the most exposed place. Without a truncated Wigner, a master equation, or at least a second-order moment test, the Fopt values in Table I are semiclassical predictions, not quantum-certified numbers.

There are also two mechanical issues that a referee should catch: Eq. (7) and (8) are misprinted (the a is missing from the coupling term in (7), and the sign of ωm in (8) is wrong), and the text says Q=10^6 in Sec III while all simulations use Q=10^4. More substantively, the paper overreaches by calling the effect 'quantum memory' and 'quantized transitions.' The memory is classical hysteresis in expectation values; the platform is quantum, but the demonstrated memory is not a quantum memory in any information-theoretic sense.

No code or data are provided, so I could not verify the numerics. The genetic algorithm optimisation reports no convergence checks, so the Fopt values could be local optima. None of these are fatal; they are addressable.

Bottom line: I would send this to a serious referee. The mean-field validation issue is the key ask. If the authors can show that the loops survive a quantum treatment (or at least clearly delimit the semiclassical domain), the paper is worth publishing. As it stands, it is a solid, useful addition to the optomechanical memristor literature, not a breakthrough.

Referee Report

3 major / 5 minor

Summary. The manuscript studies a single-mode cavity optomechanical system driven by pulsed laser fields, considering three pulse families: Gaussian trains, sinusoidal, and square-sinusoidal drives. Within a mean-field approximation for the first-order quadratures, the authors derive nonlinear equations of motion, identify hysteresis loops in the photon and phonon number versus input field, and classify the responses into single-, double-, and n-loop regimes as well as energy-storing and energy-non-storing behaviors. They introduce a dimensionless geometric form factor F to quantify memory efficiency, optimize F over pulse parameters with a genetic algorithm, and report optimal values up to Fopt = 0.965 for square-sinusoidal photonic driving, comparing favorably with several quantum memristor platforms from the literature. The central qualitative claim is that pulsed optomechanical systems can serve as programmable memory elements whose behavior is controlled by pulse shaping.

Significance. If the mean-field results are robust, the paper offers a useful and fairly systematic protocol-level study of hysteretic memory in driven-dissipative optomechanics, with a practical metric for comparing memory efficiency across platforms. The phonon convolution form in Eq. (10) follows directly from the Heisenberg equations, the classification of single-, double-, and n-loop hysteresis is clearly presented, and the optimization over pulse families is a sensible way to benchmark memory content. The main limitations are that the quantitative claims rest entirely on a semiclassical factorization whose validity is not checked in the high-cooperativity regime used for the headline numbers, and that the exactness of the photon convolution form in Eq. (9) is not established as stated. The paper does not provide code, data, or convergence statistics, so the numerical optimizations in Table I cannot be independently verified.

major comments (3)

[Sec. IV, Eqs. (15)-(18), Sec. VI E, Table I] All quantitative memory claims, including the optimized form factors in Table I, are obtained from the mean-field equations (15)-(18), yet the only justification offered is a citation to Ref. [34] for a related but distinct regime. For the relevant optimized operating point (gm = 10^-5 kappa, Q = 10^4, omega_m = 20 kappa, and <a^dag a> of order 10^11), the linearized optomechanical coupling is G = gm sqrt(<a^dag a>) ~ 3 kappa, while the mechanical damping is gamma_m = 2 x 10^-3 kappa; the resulting cooperativity is of order 10^4. In this high-cooperativity driven-dissipative regime there is no evident small parameter suppressing the neglected second-order correlations such as <delta X_m delta P_c>. The risk is especially acute near the 'dynamical quantized jumps' of Sec. VI E, where the deterministic flow is multistable and fluctuations can select between basins. I request an explicit convergence check, for example truncated-Wigner or second-order cumulant simulations, showing that the reported loops and the Fopt values are stable when leading quantum correlations are included.
[Sec. III, Eqs. (7)-(9), Appendix A] The convolution form (9) for the mean photon number is not an exact identity at the operator level. From Eq. (7), d<a^dag a>/dt = -2 kappa <a^dag a> + E(t)<a + a^dag> + i gm <a^dag(b + b^dag) - (b + b^dag)a>; the final interaction term is not generally zero and is dropped in Eq. (9). Equation (19) is a valid consequence of the mean-field equations (15)-(18) because the interaction contributions cancel in the equation for (X_c^2 + P_c^2)/2, but it is not an independent exact result. The text should clarify that Eqs. (9)-(10) are mean-field results, and Appendix A, which uses Eq. (9) to compute the photonic response to a delta pulse, should be re-derived or explicitly qualified as a mean-field statement.
[Sec. VII A, Table I] The headline values Fopt = 0.965 and Fopt = 0.963 are maxima by construction because the form factor F is both the defined measure of memory efficiency and the objective being optimized; this is not circular for the existence of nonzero hysteresis loops, but it means the numerical values are not independent predictions. The cross-platform comparison in Table I is therefore only meaningful if the optimization has genuinely converged. The manuscript reports the population size and maximum generation count of the genetic algorithm but provides no convergence statistics, no repeated runs, no standard deviations, and no code or data. I ask for a robustness analysis, such as best/mean/standard deviation over independent optimization runs and the evolution of the cost function C(theta), to support the optimal parameters in Table I.

minor comments (5)

[Sec. III] The text states 'We set Q = 10^6 in this work to realize realistic numerical simulations,' but all figures and Table I use Q = 10^4; this inconsistency should be corrected.
[Sec. VII B] The text reports a phonon form factor of 0.4441 for sinusoidal driving, while Table I lists 0.441; these numbers should be reconciled.
[Sec. II, Eq. (5)] The statement that 0 <= F <= 1 follows from the isoperimetric inequality applies to simple closed curves; for the self-intersecting multi-loop trajectories discussed in Sec. VI D, the inequality should be stated with the appropriate caveat or restricted to the single-loop optimization in Sec. VII.
[Ref. [50]] Reference [50] is an augmented Lagrangian barrier algorithm paper and does not appear to describe a genetic algorithm; a proper reference for the genetic-algorithm method is needed.
[Sec. VI E] The term 'dynamical quantized jumps' may mislead readers: the jumps in Fig. 5 are discrete plateaus in the mean phonon number of a deterministic mean-field model and are not shown to be quantum jumps; a term such as 'amplitude-locked plateaus' or an explicit qualification would be more accurate.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: hysteresis and form-factor values are computed from the stated mean-field equations and a defined geometric metric, not fitted inputs or self-citation chains.

full rationale

The paper's central results are self-contained numerical evaluations. The mean-field equations (15)-(18) follow from the Hamiltonian (6) by dropping second-order fluctuation correlations; no parameter is fitted to the reported form factors. The form factor F in Eq. (5) is introduced as a geometric metric defined by the area and perimeter of the computed input-output trajectory, and Sec. VII A optimizes that metric over drive parameters. Reporting the optimized value is the normal evaluation of a defined figure of merit, not a prediction forced by construction: the nonzero loop areas, the energy-storing/non-storing distinction, and the multi-loop and jump structures all emerge from the dynamics rather than being imposed by the metric. The citations [1], [34], and [44] supply background definitions, a mean-field validity argument, and an optimization method, respectively. Although [34] is prior work by one coauthor, it is independent published support and does not contain the target result, so the load-bearing argument does not reduce to an unverified self-citation. Any concern about the accuracy of the mean-field truncation at high cooperativity is a validity or robustness issue, not a circularity, and therefore does not raise the circularity score.

Assumptions & free parameters 10 free parameters · 6 assumptions · 0 invented entities

The paper's quantitative claims rest on mean-field dynamics, the chosen form-factor metric, and hand-picked simulation parameters; no experimental or first-principles quantum check is provided.

free parameters (10)

Gaussian train amplitude E0 = 5.717e5 κ (photons); 2.015e5 κ (phonons)
Optimized in Table I to maximize form factor, not fixed by an experimental constraint.
Gaussian train pulse separation ts = 16.119 κ^-1 (photons); 30.974 κ^-1 (phonons)
Optimized in Table I; controls adiabaticity and memory.
Gaussian train pulse width sigma = 0.313 κ^-1 (photons); 0.224 κ^-1 (phonons)
Optimized in Table I; narrowness determines non-adiabatic drive.
Sinusoidal drive amplitude E0 = 8.745e4 κ (photons); 7.895e4 κ (phonons)
Optimized in Table I to maximize F for a pinched loop.
Sinusoidal drive frequency omega = 1.055 κ (photons); 1.918 κ (phonons)
Optimized in Table I; frequency relative to ωm determines response.
Square-sinusoidal amplitude E0 = 7.498e5 κ (photons); 2.173e5 κ (phonons)
Optimized in Table I; produces the highest F values.
Square-sinusoidal frequency omega = 1.644 κ (photons); 2.794 κ (phonons)
Optimized in Table I; sharp inflection points enhance temporal asymmetry.
Mechanical quality factor Q = 10^4 (figures and Table I); Sec. III text says 10^6
Chosen by hand; inconsistent across the paper.
Optomechanical coupling gm = 10^-5 κ (figures and simulations)
Chosen small; not matched to a specific experimental gm range cited in Sec. III.
Mechanical frequency ωm = 20 κ
Chosen simulation parameter; sets the sideband regime.

assumptions (6)

domain assumption Markovian dissipation of cavity and mechanics with rates κ and γm in Heisenberg-Langevin form
Eqs. (7)-(8); standard but neglects structured environments and non-Markovian baths.
domain assumption Mean-field factorization ⟨AB⟩ ≈ ⟨A⟩⟨B⟩
Sec. IV; valid if fluctuations are small, but not checked against a quantum master equation in the strong-drive regime.
domain assumption Form factor F = 4πA/P² measures memory efficiency
Borrowed from Ref. [44]; assumes loop area captures time non-locality and isoperimetric bound applies to all loops including self-intersecting ones.
domain assumption Resonant detuning Δ = 0 maximizes memory
Sec. IV states this without a derivation.
domain assumption Vacuum initial state for cavity and mechanics
Sec. III; isolates driving-induced memory but ignores thermal mechanical noise.
ad hoc to paper Chosen simulation parameters (gm = 10^-5 κ, Q = 10^4, ωm = 20 κ) are representative of current optomechanical platforms
Secs. III and V; the 'readily compatible' claim rests on this, but no specific experimental realization is modeled.

how reviews work

0 comments

Cite this review

Pith. "Pith review of Memory effects in pulsed optomechanical systems." pith.science (2026). https://pith.science/paper/Q7MIUOGY

@misc{pith2026250603455,
  author       = {Pith},
  title        = {Pith review of: Memory effects in pulsed optomechanical systems},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/Q7MIUOGY}},
  note         = {Machine review of arXiv:2506.03455}
}

read the original abstract

Memory, understood as time non-locality, is a fundamental property of any physical system, whether classical or quantum, and has important applications in a wide variety of technologies. In the context of quantum technologies, systems with memory can be used in quantum information, communication, and sensing. Here, we demonstrate that cavity optomechanical systems driven by a pulsed laser can operate as programmable quantum memory elements. By engineering the adiabatic and non-adiabatic pulses, particularly the Gaussian and sinusoidal, we induce and control diverse memory phenomena such as dynamical hysteresis, quantized phononic transitions, and distinct energy-storing responses. Within a mean-field approach, we derive the analytical and numerical criteria under which the photonic and phononic observables manifest the memory effects in strongly driven regimes. The memory effects are quantified through a dimensionless geometric form factor, which provides a versatile metric to characterize the memory efficiency. Our protocol is readily compatible with the current optomechanical platforms, highlighting the new possibilities for advanced memory functionalities in quantum technologies.

Figures

Figures reproduced from arXiv: 2506.03455 by the authors.

**Figure 2.** FIG. 2. (a) Schematic of the optomechanical setup driven by a [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗

**Figure 3.** FIG. 3. Memory responses induced by the Gaussian train pulse defined in Eq. ( [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗

Figures from the paper (3 more)

**Figure 4.** Figure 4: FIG. 4 [PITH_FULL_IMAGE:figures/full_fig_p006_4.png]

**Figure 5.** Figure 5: FIG. 5. Dynamical jumps in the mean number of phonons induced by a Gaussian train pulse in the large amplitude regime. Temporal evolution [PITH_FULL_IMAGE:figures/full_fig_p007_5.png]

**Figure 6.** Figure 6: FIG. 6. Optimal memory responses via maximization of the form factor [PITH_FULL_IMAGE:figures/full_fig_p008_6.png]

Discussion (0). Sign in to comment.

Reference graph

Works this paper leans on

51 extracted references · 50 canonical work pages

[34]

Y . Wu, G. Li, B. He, and Q. Lin, Amplitude and phase locking of mechanical oscillation driven by radiation pressure , Phys. Rev. A 105, 013521 (2022)

work page 2022
[1]

Di Ventra and Y

M. Di Ventra and Y . V . Pershin, Memristors and Memele- ments: Mathematics, Physics and Fiction , Springer, Switzer- land (2023)

work page 2023
[2]

Y . V . Pershin and M. Di Ventra,Memory effects in complex ma- terials and nanoscale systems, Adv. Phys. 60, 145 (2011)

work page 2011
[3]

Hoffmann, Spin Hall Effects in Metals , IEEE Transactions on Magnetics 49, 5172 - 5193 (2013)

A. Hoffmann, Spin Hall Effects in Metals , IEEE Transactions on Magnetics 49, 5172 - 5193 (2013)

work page 2013
[4]

Di Ventra, Y

M. Di Ventra, Y . V . Pershin, and L. O. Chua, Circuit elements with memory: memristors, memcapacitors, and meminductors , Proc. IEEE 97, 1717 (2009)

work page 2009
[5]

Martinez-Rincon and Y

J. Martinez-Rincon and Y . V . Pershin, Bistable Nonvolatile Elastic-Membrane Memcapacitor Exhibiting a Chaotic Behav- ior, IEEE Transactions on Electron Devices 58, 1809-1812 (2011)

work page 2011
[6]

Bagheri, M

M. Bagheri, M. Poot, M. Li, W. P. H. Pernice, and H. X. Tang, Dynamic manipulation of nanomechanical resonators in the high-amplitude regime and non-volatile mechanical mem- ory operation, Nature Nanotech. 6, 726-732 (2011)

work page 2011
[7]

Markovi ´c, A

D. Markovi ´c, A. Mizrahi, D. Querlioz, D. et al., Physics for neuromorphic computing, Nat. Rev. Phys. 2, 499-510 (2020)

work page 2020

Show all 51 references

[8]

Lukosevicius and H

M. Lukosevicius and H. Jaeger, Reservoir computing ap- proaches to recurrent neural network training , Computer Sci- ence Review 3, 127 (2009)

2009
[9]

Xiao-Liang Zhang, Can Geng, Jia-Mei Nie, and Qiao Gao, The missing mem-inerter and extended mem-dashpot found , Non- linear Dyn 101, 835-856 (2020)

2020
[10]

Advances in Mechan- ical Engineering 10 6 (2018)

Xiao-liang Zhang, Qiao Gao, and Jiamei Nie, The mem-inerter: A new mechanical element with memory. Advances in Mechan- ical Engineering 10 6 (2018)

2018
[11]

Jin-Song Pei, Mem-spring models combined with hybrid dy- namical system approach to represent material behavior, Jour- nal of Engineering Mechanics 144 12 (2018)

2018
[12]

Di Ventra, MemComputing: Fundamentals and Applica- tions (Oxford University Press, Oxford, 2022)

M. Di Ventra, MemComputing: Fundamentals and Applica- tions (Oxford University Press, Oxford, 2022)

2022
[13]

M. M. Wolf, J. Eisert, T. S. Cubitt, and J. I. Cirac, Assess- ing non-Markovian quantum dynamics , Phys. Rev. Lett. 101, 150402 (2008)

2008
[14]

Breuer, E.-M

H.-P. Breuer, E.-M. Laine, and J. Piilo, Measure for the degree of non-Markovian behavior of quantum processes in open sys- tems, Phys. Rev. Lett. 103, 210401 (2009)

2009
[15]

F. F. Fanchini, G. Karpat, D. Z. Rossatto, A. Norambuena, and R. Coto, Estimating the degree of non-Markovianity using ma- chine learning, Phys. Rev. A 103, 022425 (2021)

2021
[16]

de Vega and D

I. de Vega and D. Alonso, Dynamics of non-Markovian open quantum systems, Rev. Mod. Phys. 89, 015001 (2017)

2017
[17]

Rivas, S

A. Rivas, S. F. Huelga, and M. B. Plenio, Quantum non- Markovianity: characterization, quantification and detection , Rep. Prog. Phys. 77, 094001 (2014)

2014
[18]

F. F. Fanchini, G. Karpat, B. C ¸ akmak, L. K. Castelano, G. H. Aguilar, O. J. Faras, S. P. Walborn, P. H. Souto Ribeiro, and M. C. de Oliveira, Non-Markovianity through accessible informa- tion, Phys. Rev. Lett. 112, 210402 (2014)

2014
[19]

Rivas, S

A. Rivas, S. F. Huelga, and M. B. Plenio, Entanglement and Non-Markovianity of Quantum Evolutions , Phys. Rev. Lett. 105, 050403 (2010)

2010
[20]

L. Li, M. J. W. Hall, and H. M. Wiseman, Concepts of quantum non-Markovianity: A hierarchy, Phys. Rep. 999, 1 (2023)

2023
[21]

Salmilehto, F

J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum memristors with superconducting circuits , Sci. Rep. 7, 42044 (2017)

2017
[22]

Kumar, F

S. Kumar, F. C ´ardenas-L´opez, N. Hegade, X. Chen, F. Al- barr´an-Arriagada, E. Solano, and G. Alvarado Barrios, Entan- gled quantum memristors, Phys. Rev. A 104, 062605 (2021)

2021
[23]

Norambuena, F

A. Norambuena, F. Torres, M. Di Ventra, and R. Coto, Polariton-based quantum memristors, Phys. Rev. Applied 17, 024056 (2022)

2022
[24]

Peotta, and M

S. Peotta, and M. Di Ventra, Superconducting Memristors , Phys. Rev. Applied 034011, 2 (2014)

2014
[25]

Y . Li, G. W. Holloway, S. C. Benjamin, G. A. D. Briggs, J. Baugh, and J. A. Mol, Double quantum dot memristor , Phys. Rev. B 96, 075446 (2017)

2017
[26]

Stremoukhov, V

S. Stremoukhov, V . I. Makarov, and V . V . Sheremet,Proposal for Trapped-Ion Quantum Memristor, Entropy 25, 1134 (2023)

2023
[27]

Tian, X.-Y

J.-L. Tian, X.-Y . Kong, S.-Y . Zhang, and X.-M. Xiu, Tunable Non-Markovianity for Bosonic Quantum Memristors , Entropy 25, 756 (2023)

2023
[28]

Y . M. Guo, F. Albarrn-Arriagada, H. Alaeian, E. Solano, and G. Alvarado Barrios, Quantum memristors with quantum comput- ers, Phys. Rev. Applied 18, 024082 (2022)

2022
[29]

M. Sanz, L. Lamata, and E. Solano, Invited Article: Quantum memristors in quantum photonics , APL Photonics 3, 080801 (2018)

2018
[30]

Spagnolo, T

M. Spagnolo, T. D’Abrosca, L. Innocenti, A. Crespi, R. Osel- lame, N. Viggianiello, V . Cimini, L. Vitagliano, G. Esposito, A. Ferraro, M. Paternostro, and F. Sciarrino,Experimental pho- tonic quantum memristor, Nat. Photonics 16, 318 (2022)

2022
[31]

Gonzalez-Raya, J

T. Gonzalez-Raya, J. M. Lukens, L. C. C ´eleri, and M. Sanz, Quantum memristors in frequency-entangled optical fields, Ma- terials 13, 864 (2020)

2020
[32]

J.-Y . Ma, H. Zhang, X. Zhang, B. Zeng, X. Zhu, J. Tang, and S. Zhang, Photonic memristor for future computing: a perspec- tive, Adv. Opt. Mater. 7, 1900766 (2019)

2019
[33]

Aspelmeyer, T

M. Aspelmeyer, T. J. Kippenberg, and F. Marquardt,Cavity op- tomechanics, Rev. Mod. Phys. 86, 1391 (2014)

2014
[35]

He and Q

B. He and Q. Lin, Dynamical approach to quantum optome- chanics: Motivation, method, and applications , Fundam. Res. 3, 1 (2023). 12

2023
[36]

He, Quantum optomechanics beyond linearization , Phys

B. He, Quantum optomechanics beyond linearization , Phys. Rev. A 85, 063820 (2012)

2012
[37]

B. He, L. Yang, Q. Lin, and M. Xiao, Radiation pressure cool- ing as a quantum dynamical process , Phys. Rev. Lett. 118, 233604 (2017)

2017
[38]

Z. X. Chen, Y . C. Liu, Y . L. Zhang, and Y . W. Lin,Entangle- ment dynamics in double-cavity optomechanical systems , Opt. Express 25, 17757 (2017)

2017
[39]

Z. F. Yan, B. He, and Q. Lin, Force sensing with an optome- chanical system at room temperature, Phys. Rev. A107, 013529 (2023)

2023
[40]

B. He, Q. Lin, M. Orszag, and M. Xiao,Mechanical oscillations frozen on discrete levels by two optical driving fields, Phys. Rev. A 102, 011503(R) (2020)

2020
[41]

Zhu, C.-S

G.-L. Zhu, C.-S. Hu, Y . Wu, X.-Y . L¨u Cavity optomechanical chaos, Fundam. Res. 3, 1 (2023)

2023
[42]

Zippilli, N

S. Zippilli, N. Kralj, M. Rossi, G. Di Giuseppe, and D. Vitali, Cavity optomechanics with feedback-controlled in-loop light , Phys. Rev. A 98, 023828 (2018)

2018
[43]

Gr ¨oblacher, A

S. Gr ¨oblacher, A. Trubarov, N. Prigge, G. D. Cole, M. As- pelmeyer, and J. Eisert, Observation of non-Markovian mi- cromechanical Brownian motion , Nat. Commun. 6, 7606 (2015)

2015
[44]

Hernani-Morales, G

C. Hernani-Morales, G. Alvarado, F. Albarr ´an-Arriagada, Y . Vives-Gilabert, E. Solano, J. D. Martn-Guerrero, Machine Learning for Maximizing the Memristivity of Single and Cou- pled Quantum Memristors , Adv. Quantum Technol. 2300294 (2024)

2024
[45]

Di Ventra, and Y

M. Di Ventra, and Y . V . Pershin, On the physical properties of memristive, memcapacitive and meminductive systems, Nan- otechnology 24, 255201 (2013)

2013
[46]

T. J. Kippenberg and K. J. Vahala, Cavity Optomechanics: Back-Action at the Mesoscale, Science 321, 5893 (2008)

2008
[47]

Vahala, Optical microcavities, Nature 424, 839-846 (2003)

K. Vahala, Optical microcavities, Nature 424, 839-846 (2003)

2003
[48]

Kimble, The quantum internet Nature 453, 1023-1030 (2008)

H. Kimble, The quantum internet Nature 453, 1023-1030 (2008)

2008
[49]

Zhang, M

J. Zhang, M. Orszag, M. Xiao, X. Jiang, Q. Lin, and B. He, Highly Correlated Optomechanical Oscillations Manifested by an Anomalous Stabilization , Phys. Rev. Lett. 133, 103602 (2024)

2024
[50]

A. R. Conn, N. I. M. Gould, and Ph. L. Toint, A Glob- ally Convergent Augmented Lagrangian Barrier Algorithm for Optimization with General Inequality Constraints and Simple Bounds, Mathematics of Computation 66, 217 261-288 (1997)

1997
[51]

Ferrara and R

A. Ferrara and R. Lo Franco, Entanglement and coherence dy- namics in photonic quantum memristors , Phys. Rev. A 111, 012421 (2025)

2025

Pith tools

Reviewed August 7, 2026 · model on record in the stance chip above.

[1] [34]

Y . Wu, G. Li, B. He, and Q. Lin, Amplitude and phase locking of mechanical oscillation driven by radiation pressure , Phys. Rev. A 105, 013521 (2022)

work page 2022

[2] [1]

Di Ventra and Y

M. Di Ventra and Y . V . Pershin, Memristors and Memele- ments: Mathematics, Physics and Fiction , Springer, Switzer- land (2023)

work page 2023

[3] [2]

Y . V . Pershin and M. Di Ventra,Memory effects in complex ma- terials and nanoscale systems, Adv. Phys. 60, 145 (2011)

work page 2011

[4] [3]

Hoffmann, Spin Hall Effects in Metals , IEEE Transactions on Magnetics 49, 5172 - 5193 (2013)

A. Hoffmann, Spin Hall Effects in Metals , IEEE Transactions on Magnetics 49, 5172 - 5193 (2013)

work page 2013

[5] [4]

Di Ventra, Y

M. Di Ventra, Y . V . Pershin, and L. O. Chua, Circuit elements with memory: memristors, memcapacitors, and meminductors , Proc. IEEE 97, 1717 (2009)

work page 2009

[6] [5]

Martinez-Rincon and Y

J. Martinez-Rincon and Y . V . Pershin, Bistable Nonvolatile Elastic-Membrane Memcapacitor Exhibiting a Chaotic Behav- ior, IEEE Transactions on Electron Devices 58, 1809-1812 (2011)

work page 2011

[7] [6]

Bagheri, M

M. Bagheri, M. Poot, M. Li, W. P. H. Pernice, and H. X. Tang, Dynamic manipulation of nanomechanical resonators in the high-amplitude regime and non-volatile mechanical mem- ory operation, Nature Nanotech. 6, 726-732 (2011)

work page 2011

[8] [7]

Markovi ´c, A

D. Markovi ´c, A. Mizrahi, D. Querlioz, D. et al., Physics for neuromorphic computing, Nat. Rev. Phys. 2, 499-510 (2020)

work page 2020