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Thermodynamics of coherent energy exchanges between lasers and two-level systems

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Pith's one-line read The paper claims that in a strongly driven qubit–laser system the apparent violation of the thermodynamic work formula disappears once work is attributed to the dressed laser rather than the original laser.

desk verdict Strong, credible resolution of the strong-drive work puzzle; the dressed-laser construction is new and the master-equation consistency program is careful, but the O(1/|alpha|) factorization error in Eq. (31) and the unbenchmarked approximation (141) need work before I'd take the generalized Bloch equation at all strengths. read the letter →

arxiv 2501.09625 v1 pith:SUIYAOA4 submitted 2025-01-16 quant-ph

Ariane Soret , Massimiliano Esposito This is my paper · ORCID
classification quant-ph
keywords quantumthermodynamicsdressedqubitlaserFloquetmasterequationfullcountingstatisticsCrooksfluctuationtheoremthermodynamicconsistencyopensystems
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

This paper aims to resolve a known inconsistency in the thermodynamics of a two-level system (qubit) driven by a strong coherent laser and coupled to a thermal bath: the work rate predicted by the standard Floquet master equation does not match the canonical expression $\mathrm{Tr}[\rho\, dV/dt]$ of quantum thermodynamics. The authors argue that the discrepancy is a bookkeeping error: once the joint qubit–laser Hilbert space is decomposed into a dressed qubit and a dressed laser (the laser state modified by the interaction), the work delivered to the dressed qubit is produced by the dressed laser, $W_{DL}=-\Delta E_{DL}$, which differs from the bare-laser work $W_L=-\Delta E_L$ by the atomic term $(\omega_L/2)\sigma_z$. Starting from a microscopic autonomous model, they derive full counting statistics for both work definitions, prove Crooks fluctuation theorems for them, and turn these theorems into consistency conditions for quantum master equations. The payoff is a new generalized Bloch equation valid at all driving strengths, a Floquet master equation shown to be fully thermodynamically consistent in the strong-drive regime, and a demonstration that the usual second-order derivation of the Bloch equation breaks the fluctuation theorems.

What carries the argument

The central object is the dressed-qubit decomposition of the joint qubit–laser Hilbert space, $H_A\otimes H_L \to H_{DA}\otimes H_{DL}$, built from the dressed states of the driven system. It converts the interacting Hamiltonian into $H_X = H_{DA}\otimes I_{DL} + I_{DA}\otimes H_{DL}$, so the dressed laser is an autonomous work source with $W_{DL} = -\Delta E_{DL}$. The identity $H_{DL} = H_L + (\omega_L/2)\sigma_z$ (on the relevant tensor factors) is the load-bearing relation: it shows exactly how dressed-laser work differs from bare-laser work and turns the apparent Floquet anomaly into a consistent work statistic. The counting-field symmetries (107), (113) and the strict energy-conservation conditions (109), (114) are the criteria that decide whether a master equation is thermodynamically consistent.

What would settle it

Compute the full counting statistics of $W_{DL}$ in the autonomous qubit-laser-bath model with the laser in a coherent state of decreasing amplitude $|\alpha|$; if the Crooks symmetry (84) fails once $\langle N\rangle$ is no longer much larger than $\sigma(N)$, the macroscopic-limit assumption fails. Alternatively, in a strongly driven superconducting or trapped-ion qubit, measure both the photon-number change of the drive mode and the dressed-qubit energy change: if $-\Delta E_{DL}$ does not equal the work inferred from the Floquet master equation, while $-\Delta E_L$ does, then the central attribution of work to the dressed laser is wrong.

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Extended reading notes

Core claim

On the paper's own terms, the central discovery is that the dressed qubit and the dressed laser are the physically correct subsystems for energy bookkeeping. Under the dressed-qubit mapping, the joint Hamiltonian splits as $H_X = H_{DA}\otimes I_{DL} + I_{DA}\otimes H_{DL}$, with $H_{DL} = I_A\otimes H_L + (\omega_L/2)\sigma_z\otimes I_L$. Energy conservation then forces the first laws $\Delta E_A = Q + W_L$ and $\Delta E_{DA} = Q + W_{DL}$, where $W_L = -\Delta E_L$ and $W_{DL} = -\Delta E_{DL}$. Because the two work definitions differ by the expectation value of $(\omega_L/2)\sigma_z$, the strong-drive work rate obtained from the Floquet master equation (its Eq. (153)) is not the canonical $\mathrm{Tr}[\rho\, dV/dt]$: it is the work produced by the dressed laser on the dressed qubit. The authors support this attribution by showing that the Floquet master equation satisfies the fluctuation-theorem symmetry (107) and the strict energy-conservation condition (109), while the optical Bloch equation satisfies the fluctuation theorems only on average; the Bloch equation obtained from the conventional second-order master equation breaks them once counting fields are included.

Load-bearing premise

The load-bearing premise is that the laser contains a macroscopic number of photons, $\langle N\rangle \gg \sigma(N) \gg 1$, so that $\sqrt{N+1}$ can be replaced by $g$ and the initial state factorizes in the dressed basis up to corrections of order $1/|\alpha|$; without it, the dressed qubit-dressed laser tensor-product split, the identification of $W_{DL}$, and the resulting fluctuation theorems all collapse.

Editorial extensions

If this is right

  • The Floquet master equation is fully thermodynamically consistent in the strong-drive regime: it obeys the counting-field symmetry (107) and strict energy conservation (109), so its first and second laws hold both on average and at the fluctuating level.
  • The optical Bloch equation derived from quantum maps satisfies the fluctuation theorems and the first and second laws on average, but not strict energy conservation; the same equation obtained from the conventional second-order master equation breaks the fluctuation theorems entirely.
  • The generalized Bloch equation is valid at all driving strengths and is fully consistent in the strong-drive limit; the Bloch and Floquet master equations emerge as its weak/intermediate and strong-coupling approximations, respectively.
  • In their common regime of validity, the Bloch and Floquet master equations give the same steady-state heat and work rates up to corrections of order $\gamma_{\max}^2/g^2$, below the accuracy of the perturbative derivation.
  • The difference between $W_L$ and $W_{DL}$, equal to the atomic term $(\omega_L/2)\sigma_z$, explains why strong-drive work is not of the canonical form $\mathrm{Tr}[\rho\, dV/dt]$.

Reading between the lines

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

  • If the dressed-laser attribution is correct, then the reported "work done by a laser on a qubit" depends on a partition choice: measuring the bare field or the dressed field gives different numbers, and experimental papers would need to state which one they track.
  • The same consistency criteria could be applied to d-level atoms, multiple lasers, or multi-mode fields; the single-mode two-level case is a minimal testbed, and a fully consistent extension is not guaranteed by the present proof.
  • The limit of low photon numbers, where the displacement term and the photon-counting term become comparable, is the natural place to falsify the macroscopic simplification: measured work statistics should deviate from the macroscopic-limit Crooks symmetry before environmental noise matters.
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Formalized claims in Lean

  1. Claim #1: On the paper's own terms, the central discovery is that the dressed qubit and the dressed laser are the physically correct subsystems for energy bookkeeping. Under the dressed-qubit mapping, the joint Hamiltonian splits as $H_X = H_{DA}\otimes I_{DL} + I_{DA}\otimes H_{DL}$, with $H_{DL} = I_A\otimes H_L + (\omega_L/2)\sigma_z\otimes I_L$. Energy conservation then forces the first laws $\Delta E_A

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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

4 major / 6 minor

Summary. The paper develops a quantum thermodynamic treatment of a two-level system (qubit) driven by a coherent laser mode and weakly coupled to a thermal bath, starting from a microscopic autonomous Hamiltonian. It introduces a dressed-qubit/dressed-laser decomposition, defines work from the laser and from the dressed laser, and derives average first and second laws together with Crooks-type fluctuation theorems for both work definitions using two-point measurements with counting fields. These fluctuation theorems are then converted into consistency criteria for quantum master equations, and the criteria are used to assess the generalized Bloch equation, the optical Bloch equation, and the Floquet master equation. The central claim is that the apparent contradiction between the work rate obtained from the Floquet master equation and the canonical expression Tr[ρ dV/dt] in the strong-driving regime is resolved by recognizing that the Floquet master equation describes work performed by the dressed laser, not by the original laser. The paper also shows that a Redfield-based derivation of the Bloch equation breaks the fluctuation theorems, whereas a quantum-map-based derivation preserves them.

Significance. If the claims hold, this paper provides a systematic framework for energy bookkeeping in strongly driven open quantum systems and resolves a long-standing discrepancy in the thermodynamic interpretation of the Floquet master equation. It derives two new symmetries, Eqs. (81) and (94), as master-equation consistency criteria; introduces a generalized Bloch equation valid at all driving strengths; and identifies the Redfield-equation origin of fluctuation-theorem violations. The derivations are largely self-contained, contain no fitted parameters, and are supported by numerical moment-generating-function checks. These are substantial contributions. However, the central interpretation relies on an uncontrolled O(1/|α|) factorization of the initial state and on an unquantified symmetrization approximation, so the main claims are not yet fully established at the quantitative level.

major comments (4)
  1. [III.B.2, Eq. (31)] The factorization of the initial state as ρ(0) = ρ_DA(0) ⊗ ρ_DL(0) ⊗ ρ_B is asserted only 'up to corrections of the order 1/|α|', and the same order of corrections is later neglected when setting β_DL = 0 after Eq. (81). Since the first law ΔE_DA = Q + W_DL, Eq. (55), and the work fluctuation theorem, Eq. (84), rely on this factorization, the residual correlation-energy terms may introduce an uncontrolled offset. The paper should provide a quantitative error estimate in terms of |α|, or benchmark the approximation against an exact simulation of the original autonomous dynamics of Eq. (15) for finite α.
  2. [V.B.1, Eq. (141)] The symmetrization approximation, which replaces sums over bath modes by products of square roots of rates and is essential for the generalized Bloch equation to satisfy the consistency conditions (107) and (113), is introduced without a derivation, an error estimate, or a precise regime of validity. Because the generalized Bloch equation is a central new result and the consistency claims for it depend directly on Eq. (141), this approximation needs a quantitative justification, for example a bound in terms of γ_max δ_0 or a numerical convergence test.
  3. [IV.B, after Eq. (109)] The statement that full thermodynamic consistency, namely conditions (107) and (109), requires the secular approximation is justified only by reference to the authors' previous work [31], with the text saying 'We do not provide a detailed proof here'. Since the full consistency of the Floquet master equation is one of the main claims of the paper, the proof should be at least sketched in the main text or an appendix, or the relevant theorem from [31] should be stated explicitly so that the present derivation can be followed without accessing the earlier paper.
  4. [Numerics (Figs. 3, 4, 7, 8)] The numerical demonstrations are all performed within the derived master equations or with a discretized bath model, but none of them compare the approximated dynamics against the exact autonomous evolution generated by the full Hamiltonian (15). In particular, the magnitude of the O(1/|α|) corrections in Eq. (31) and the error introduced by the symmetrization approximation in Eq. (141) are never quantified. A numerical benchmark for finite α, for example a simulation of the full qubit-laser-bath unitary dynamics or a numerically exact method, is needed to support the central physical interpretation that W_DL is the work delivered to the dressed qubit and produced by the dressed laser.
minor comments (6)
  1. [II.B.2, Eq. (13)] In the sentence introducing Eq. (13), the symbol Gpoi(λ, t) is used twice; the second occurrence should be Gcoh(λ, t), the generating function for a coherent state.
  2. [V.B.2, last paragraph] The sentence 'which partially explains the difference from the anticipated form (153)' refers to Eq. (63), not Eq. (153), and the cross-reference should be corrected.
  3. [Figure 7 caption] The legend labels are difficult to distinguish, and some labels such as 'log G(λDL)' and 'log GGME,R(λDL)' appear more than once; please clarify which curves correspond to which master equation and which are forward versus reversed.
  4. [Table I] The table contains a typo ('Weak/intermdediate') and the abbreviations S.D. and W.D. are not defined in the caption; please define them and correct the spelling.
  5. [III.D.1, Eq. (52)] The index n is used both for the dressed-laser Fock states and as the summation index in the same equation, which may confuse the reader; consider using a different symbol for the sum.
  6. [II.B] The claim that a coherent state and a Poisson state are equivalent for work statistics is supported by Fig. 1, but no quantitative statement of the expected error scale in the moments beyond the average is given; a brief estimate of the correction order would be helpful.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the dressed-laser work attribution is an exact operator identity, and the consistency analyses are explicit; self-citation to [31] is independent published support, not a circular input.

full rationale

The derivation chain is self-contained for the central claim. The split H_X = H_DA + H_DL is obtained from an explicit dressed-state transformation, Eqs. (26)-(30), and the first laws (49) and (55) follow from energy conservation with Q defined via the bath. The relation W_DL = W_L - Tr[(omega_L/2) sigma_z Delta rho], Eq. (57), is an exact consequence of H_DL = H_L + (omega_L/2) sigma_z, Eq. (32), not a fitted or assumed relation. The fluctuation-theorem symmetries (81) and (94) are derived in Appendices D and E from the tilted unitary dynamics with the stated macroscopic-coherent-state and initial-state assumptions; they are then used as criteria, and the master equations are checked against them explicitly, e.g., the Floquet dissipator in Appendix H satisfies the strict energy conservation condition (109) by direct inspection of Eq. (H4). The only notable self-citation is the import of the consistency condition (102) and the secular-approximation uniqueness statement from Ref. [31]: the paper says "We do not provide a detailed proof here since the reasoning and calculations are almost identical as in [31]". This is a proof deferral to prior same-author work, but Ref. [31] is a parameter-free published derivation with stated assumptions that do not contain the present dressed-laser result; it therefore counts as independent support and does not make the argument circular. The O(1/|alpha|) correction to the dressed-basis factorization, Eq. (31), is a quantitative robustness issue that is not controlled numerically against the original autonomous dynamics, but this is a correctness or validation concern, not a reduction of the paper's results to their own inputs.

Assumptions & free parameters 0 free parameters · 8 assumptions · 1 invented entities

No free parameters are fitted to data; g0, gk, alpha, beta_B, and the bath spectral function are physical or numerical inputs. The central claims rest on standard open-quantum-system approximations and on the macroscopic-laser assumption. The main technical ingredient not proven in this paper is the secular-approximation lemma imported from the authors' earlier work [31].

assumptions (8)
  • domain assumption Assumption 1: near resonance, omega_L >> |omega_L - omega_A|, justifying the rotating-wave approximation.
    Section III.B.1 drops counter-rotating terms so that H_X becomes block diagonal in the subspaces spanned by |b,N> and |a,N+1>.
  • domain assumption Assumption 2: macroscopic laser, <N> >> sigma(N) >> 1, so that sqrt(N+1) is replaced by g and the dressed-basis initial state factorizes up to O(1/|alpha|).
    Used in Eq. (24) and Eq. (31); this is the weakest load-bearing premise of the paper.
  • domain assumption Weak coupling to the thermal bath and a Markovian semigroup hypothesis for the quantum maps.
    Section IV.A, Eqs. (99) to (101), is the basis for all the master equations derived later.
  • domain assumption Strong-driving secular approximation and the coarse-graining time-scale hierarchy (140).
    Section V.B uses omega_L, omega_A, Omega >> delta_0^-1 >> gamma_max to reduce the generalized Bloch equation to the Floquet equation.
  • domain assumption Smooth spectral density assumption G_+(omega_L), G_+(omega_L +/- Omega) approximately equal to G_+(omega_A) for the Bloch equation.
    Eq. (157) restricts the Bloch master equation to weak, intermediate, and common regimes and is not valid for structured spectral densities.
  • domain assumption A Poisson photon state is represented as a Gaussian, which is in turn represented as a Gibbs state with beta_DL = 1/|alpha|^2, and then beta_DL is taken to zero.
    Appendix D, Eq. (80), is used to prove the fluctuation symmetry (81) and hence the Crooks relation for the dressed laser.
  • domain assumption Initial thermal states for the fluctuation theorems: rho_DA(0) proportional to exp(-beta_DA H_DA), a thermal bath, and the reverse-process initial conditions in Eqs. (79) and (93).
    These are standard Crooks-type initial conditions but they are imposed rather than derived, and they restrict the validity of the fluctuation theorems.
  • domain assumption Neglect of the Lamb shift contribution.
    Stated in Section V.A as negligibly small; standard in this literature, but it is an approximation within the derived master equations.
invented entities (1)
  • Dressed laser subsystem H_DL with Fock basis |n>
    purpose: Identifies the work source for the dressed qubit: W_DL = -Delta E_DL is the work delivered to the dressed qubit in the strong-driving description.
    The dressed laser is not a new physical particle or force; it is a new tensor-factor decomposition of the joint qubit-laser Hilbert space, Eq. (29). Its thermodynamic role is derived within the model and is not independently observed outside this paper.

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Pith. "Pith review of Thermodynamics of coherent energy exchanges between lasers and two-level systems." pith.science (2026). https://pith.science/paper/SUIYAOA4

@misc{pith2026250109625,
  author       = {Pith},
  title        = {Pith review of: Thermodynamics of coherent energy exchanges between lasers and two-level systems},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/SUIYAOA4}},
  note         = {Machine review of arXiv:2501.09625}
}
read the original abstract

We study the quantum thermodynamics of a coherent macroscopic electromagnetic field (laser) coupled to a two-level system (qubit) near resonance, from weak to strong driving regimes. This combined system is, in turn, weakly coupled to a thermal radiation field, and can be described by an autonomous quantum master equation. We show that the laser acts as an autonomous work source and that, in the macroscopic limit, the work produced is independent of the phase of the laser. Using the dressed qubit approach, we show that the variation of energy in the laser is not the work transferred to the dressed qubit, which is instead obtained from the ''dressed laser'' -- a coherent superposition of the laser and the qubit. Using a two-point measurement technique with counting fields, we obtain the full counting statistics for the work of the laser and dressed laser, and show that they satisfy Crooks fluctuation theorems. We then use these theorems as criteria to investigate the thermodynamic consistency of quantum master equations, first in the autonomous setup for the combined system, then in the non-autonomous setup where the coherent field is eliminated and effectively described by a time dependent external field. Treating the laser as an external field in known to yield expressions for the work which are in contradiction with quantum thermodynamics predictions in the strong drive regime. We show that these inconsistencies stem from a confusion between the laser and dressed laser, and show how to correct them. We also derive a new master equation, thermodynamically consistent at all driving regimes, from which the Bloch and Floquet master equations can be obtained using additional approximations (of which we also examine the consistency).

Figures

Figures reproduced from arXiv: 2501.09625 by the authors.

Figure 1
Figure 1. FIG. 1. Ratio of the variation of the von Neumann entropy [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. Schematic representation of the mapping to the [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. Work [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗
Figures from the paper (5 more)
Figure 4
Figure 4. Figure 4: FIG. 4. Dashed line: coherences in the dressed qubit basis; [PITH_FULL_IMAGE:figures/full_fig_p008_4.png]
Figure 5
Figure 5. Figure 5: FIG. 5. Summary of the laws of thermodynamics and identities at the unitary level. (a) In the situation 1, [PITH_FULL_IMAGE:figures/full_fig_p010_5.png]
Figure 6
Figure 6. Figure 6: FIG. 6. Schematic representation of the approximations performed in order to derive the generalized Bloch, Bloch and Floquet [PITH_FULL_IMAGE:figures/full_fig_p014_6.png]
Figure 7
Figure 7. Figure 7: FIG. 7. Work [PITH_FULL_IMAGE:figures/full_fig_p023_7.png]
Figure 8
Figure 8. Figure 8: FIG. 8. Steady-state moment generating functions for the work [PITH_FULL_IMAGE:figures/full_fig_p024_8.png]

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Works this paper leans on

64 extracted references · 52 canonical work pages · cited by 1 Pith paper

  1. [31]

    Esposito, U

    M. Esposito, U. Harbola, and S. Mukamel, Nonequilibrium fluctuations, fluctuation theorems, and counting statistics in quantum systems, Reviews of modern physics 81, 1665 (2009)

    work page 2009

  2. [1]

    Summary of the approximations used to derive the Bloch and Floquet master equations, of their regimes of validity and of their thermodynamic consistency

    Generalized Bloch equation In order to derive the generalized Bloch equation, we do the following approximation, inspired by the proce- 17 Driving Weak Ω < γmax Intermediate Ω ∼ γmax (Common regime of validity) ωL, ωA ≫ Ω ≫ γmax Strong ωL, ωA, Ω ≫ γmax Time scales ωL, ωA ≫ δ−1 0 ≫ Ω, γmax ωL, ωA ≫ δ−1 0 > Ω, γmax ωL, ωA ≫ Ω ≫ δ−1 0 ≫ γmax ωL, ωA, Ω ≫ δ−1 ...

    work page

  3. [2]

    autonomous Floquet

    Strong qubit-laser coupling: Floquet ME We consider here the strong driving regime, defined in (140). In this case, the product of sinc functions (141) is non zero only in the case α = α′, which is equivalent to the secular approximation [2]. Performing the secular approximation on (142), we obtain (see appendix H for the full expression) dˆρλ DA dt = LaF...

    work page

  4. [3]

    G” for generalized Bloch, “F

    Weak and intermediate coupling: Bloch ME We now consider the weak driving regime defined in (140). Provided that G±(ν) are smooth on the intervals [±ωL − Ω, ±ωL + Ω], we may replace G±(ωL), G±(ωL ± Ω) ≈ G±(ωA) ≡ G± (157) in (142), which yields the tilted master equation dt ˆρλ DA(t) ≡ LaB λ (ˆρDA(t)) (see Appendix J for the explicit expression). When the ...

    work page

  5. [4]

    Generalized Bloch equation Using (142), (165) and (166), we obtain the generalized Bloch equation with counting fields λ = (λL, λB), LG λ (ˆ˜ρA(t)) = (168) − i[ ˆHA(t + λL/2)ˆ˜ρA(t) − ˆ˜ρA(t) ˆHA(t − λL/2)] + DGλ + (ˆ˜ρA(t)) + DGλ − (ˆ˜ρA(t)) (169) where we note ˆHA(t) ≡ ˆHA + ˆV (t) . (170) In the weak driving regime, DGλ + (ˆρ) = ˆT λ + (t)ˆρ ˆT −λ† + (...

    work page

  6. [5]

    Floquet master equation The strong coupling limit in the non-autonomous de- scription leads to the Floquet quantum master equation [5, 7]. We obtain it from (149), using the correspondence (165), LF (ˆ˜ρA(t)) = −i[ ˆHA + ˆV (t), ˆ˜ρA(t)] + DF (ˆ˜ρA(t)) (172) where the dissipator is obtained by replacing the opera- tors ˆΣz, ˆΣ± in (150) by ˆΣz(t), ˆΣ±(t),...

    work page

  7. [6]

    smooth enough

    Bloch master equation In the non-autonomous picture, the weak/intermediate driving regimes correspond to the regimes of validity of the optical Bloch master equation [3, 5]. Using (165) with (158), we obtain the optical Bloch master equation [3] LB(ˆ˜ρA(t)) = − i[ ˆHA + ˆV (t), ˆ˜ρA(t)] (179) + G+Dˆσ− (ˆ˜ρA(t)) + G−Dˆσ+ (ˆ˜ρA(t)) . From the discussion in ...

    work page arXiv 2000

  8. [7]

    This straightforward using the facts that eiωL ˆσzt/2( ˆHA + ˆV (t))e−iωL ˆσzt/2 = ˆHDA + ωL 2 ˆσz (B1) and −i∂te−iωL ˆσzt/2|j⟩ = − ωL 2 ˆσze−iωL ˆσzt/2|j⟩

    Proof of (40) In order to prove the relation (40), it is sufficient to show that the states e−iωL ˆσzt/2|j⟩, j = 1, 2, are solutions of the eigenvalue problem (39). This straightforward using the facts that eiωL ˆσzt/2( ˆHA + ˆV (t))e−iωL ˆσzt/2 = ˆHDA + ωL 2 ˆσz (B1) and −i∂te−iωL ˆσzt/2|j⟩ = − ωL 2 ˆσze−iωL ˆσzt/2|j⟩ . (B2) Indeed, replacing |uj(t)⟩ = e...

    work page

Show all 64 references
  1. [8]

    g Ω G+(ωL − Ω) Ω − δ 2Ω 2 + δg 2Ω2 p G+(ωL)G+(ωL + Ω)Ω + δ Ω # + P12(t)

    Proof of (45) We now show that the relation (40) implies that the evolution of the system in the dressed basis, in the autonomous picture, is equivalent to the evolution in the rotating frame, in the non-autonomous picture. We start with the simple case where the bath is not t...

  2. [9]

    D. D.F. Walls and G. J. Milburn, Quantum Optics (Springer, 2008)

    2008

  3. [10]

    Breuer, F

    H.-P. Breuer, F. Petruccione, et al. , The theory of open quantum systems (Oxford University Press on Demand, 2002)

    2002

  4. [11]

    Cohen-Tannoudji, J

    C. Cohen-Tannoudji, J. Dupont-Roc, and G. Grynberg, Atom-Photon Interactions: Basic Processes and Applications (Wiley, Leipzig, 1998)

    1998

  5. [12]

    A. G. Redfield, Nuclear magnetic resonance saturation and rotary saturation in solids, Phys. Rev. 98, 1787 (1955)

    1955

  6. [13]

    Elouard, D

    C. Elouard, D. Herrera-Marti, M. Esposito, and A. Auffeves, Thermodynamics of optical bloch equations, New Journal of Physics 22, 103039 (2020)

    2020

  7. [14]

    Szczygielski, D

    K. Szczygielski, D. Gelbwaser-Klimovsky, and R. Alicki, Markovian master equation and thermodynamics of a two-level system in a strong laser field, Phys. Rev. E 87, 012120 (2013)

    2013

  8. [15]

    Langemeyer and M

    M. Langemeyer and M. Holthaus, Energy flow in periodic thermodynamics, Phys. Rev. E 89, 012101 (2014)

    2014

  9. [16]

    Mori, Floquet states in open quantum systems, Annual Review of Condensed Matter Physics 14, 35 (2023), https://doi.org/10.1146/annurev-conmatphys-040721-015537

    T. Mori, Floquet states in open quantum systems, Annual Review of Condensed Matter Physics 14, 35 (2023), https://doi.org/10.1146/annurev-conmatphys-040721-015537

    2023 doi

  10. [17]

    J. H. Shirley, Solution of the schr¨ odinger equation with a hamiltonian periodic in time, Phys. Rev. 138, B979 (1965)

    1965

  11. [18]

    Allen and J

    L. Allen and J. H. Eberly, Optical resonance and two-level atoms (1975)

    1975

  12. [19]

    E. Geva, R. Kosloff, and J. L. Skinner, On the relaxation of a two-level system driven by a strong electromagnetic field, The Journal of Chemical Physics 102, 8541 (1995), https://pubs.aip.org/aip/jcp/article- pdf/102/21/8541/9434955/8541 1 online.pdf

    1995

  13. [20]

    Bulnes Cuetara, A

    G. Bulnes Cuetara, A. Engel, and M. Esposito, Stochastic thermodynamics of rapidly driven systems, New J. Phys. 17, 055002 (2015)

    2015

  14. [21]

    P. P. Hofer, M. Perarnau-Llobet, L. D. M. Miranda, G. Haack, R. Silva, J. B. Brask, and N. Brunner, Markovian master equations for quantum thermal machines: local versus global approach, New Journal of Physics 19, 123037 (2017)

    2017

  15. [22]

    S. P. Prasad, M. Maffei, P. A. Camati, C. Elouard, and A. Auff` eves, Closing optical bloch equations in waveguide qed: Dynamics, energetics, (2024)

    2024

  16. [23]

    Uzdin, A

    R. Uzdin, A. Levy, and R. Kosloff, Equivalence of quantum heat machines, and quantum-thermodynamic signatures, Phys. Rev. X 5, 031044 (2015). 38

    2015

  17. [24]

    Uzdin, Coherence-induced reversibility and collective operation of quantum heat machines via coherence recycling, Phys

    R. Uzdin, Coherence-induced reversibility and collective operation of quantum heat machines via coherence recycling, Phys. Rev. Appl. 6, 024004 (2016)

    2016

  18. [25]

    Klatzow, J

    J. Klatzow, J. N. Becker, P. M. Ledingham, C. Weinzetl, K. T. Kaczmarek, D. J. Saunders, J. Nunn, I. A. Walmsley, R. Uzdin, and E. Poem, Experimental demonstration of quantum effects in the operation of microscopic heat engines, Phys. Rev. Lett. 122, 110601 (2019)

    2019

  19. [26]

    Donvil, Thermodynamics of a periodically driven qubit, Journal of Statistical Mechanics: Theory and Experiment 2018, 043104 (2018)

    B. Donvil, Thermodynamics of a periodically driven qubit, Journal of Statistical Mechanics: Theory and Experiment 2018, 043104 (2018)

    2018

  20. [27]

    Restrepo, J

    S. Restrepo, J. Cerrillo, P. Strasberg, and G. Schaller, From quantum heat engines to laser cooling: Floquet theory beyond the born–markov approximation, New Journal of Physics 20, 053063 (2018)

    2018

  21. [28]

    Zhang, J

    J. Zhang, J. Zhang, and G. e. a. Ding, Dynamical control of quantum heat engines using exceptional points, Nat. Commun. 13, 6225 (2022)

    2022

  22. [29]

    Spohn and J

    H. Spohn and J. L. Lebowitz, Irreversible thermodynamics for quantum systems weakly coupled to thermal reservoirs, Adv. Chem. Phys 38, 109 (1978)

    1978

  23. [30]

    Alicki, The quantum open system as a model of the heat engine, Journal of Physics A: Mathematical and General 12, L103 (1979)

    R. Alicki, The quantum open system as a model of the heat engine, Journal of Physics A: Mathematical and General 12, L103 (1979)

    1979

  24. [32]

    Strasberg, G

    P. Strasberg, G. Schaller, T. Brandes, and M. Esposito, Quantum and information thermodynamics: A unifying framework based on repeated interactions, Phys. Rev. X 7, 021003 (2017)

    2017

  25. [33]

    Engelhardt, S

    G. Engelhardt, S. Choudhury, and W. V. Liu, Unified light-matter floquet theory and its application to quantum commu- nication (2023), arXiv:2207.08558 [quant-ph]

    2023 arXiv

  26. [34]

    Engelhardt, J

    G. Engelhardt, J. Luo, V. M. Bastidas, and G. Platero, Photon-resolved floquet theory in open quantum systems (2023), arXiv:2311.01509 [quant-ph]

    2023 arXiv

  27. [35]

    B. R. Mollow, Pure-state analysis of resonant light scattering: Radiative damping, saturation, and multiphoton effects, Phys. Rev. A 12, 1919 (1975)

    1975

  28. [36]

    To obtain the expression for ˆ˜H(t), we used ˆD†(α(t)) ˆHL ˆD(α(t)) = ˆHL + ωL(α(t)∗ˆa + α(t)ˆa† + |α|2) and −i∂t( ˆD†(α(t))) ˆD(α(t)) = ωL(α(t)∗ˆa + α(t)ˆa† + |α|2)

  29. [37]

    Esposito, K

    M. Esposito, K. Lindenberg, and C. Van den Broeck, Entropy production as correlation between system and reservoir, New Journal of Physics 12, 013013 (2010)

    2010

  30. [38]

    Avanzini et

    F. Avanzini et. al., Methods and conversations in (post)modern thermodynamics, SciPost Phys. Lect. Notes , 80 (2024)

    2024

  31. [39]

    Soret, V

    A. Soret, V. Cavina, and M. Esposito, Thermodynamic consistency of quantum master equations, Phys. Rev. A 106, 062209 (2022)

    2022

  32. [40]

    G. E. Crooks, Entropy production fluctuation theorem and the nonequilibrium work relation for free energy differences, Physical Review E 60, 2721 (1999)

    1999

  33. [41]

    Tasaki, Jarzynski relations for quantum systems and some applications (2000), arXiv:cond-mat/0009244 [cond-mat.stat- mech]

    H. Tasaki, Jarzynski relations for quantum systems and some applications (2000), arXiv:cond-mat/0009244 [cond-mat.stat- mech]

    2000 arXiv

  34. [42]

    Jarzynski, Nonequilibrium equality for free energy differences, Physical Review Letters 78, 2690 (1997)

    C. Jarzynski, Nonequilibrium equality for free energy differences, Physical Review Letters 78, 2690 (1997)

    1997

  35. [43]

    J. W. Farley and W. H. Wing, Accurate calculation of dynamic stark shifts and depopulation rates of rydberg energy levels induced by blackbody radiation. hydrogen, helium, and alkali-metal atoms, Phys. Rev. A 23, 2397 (1981)

    1981

  36. [44]

    Carmichael, Statistical Methods in Quantum Optics 1: Master Equations and Fokker–Planck Equations (Springer, Berlin, 2002)

    H. Carmichael, Statistical Methods in Quantum Optics 1: Master Equations and Fokker–Planck Equations (Springer, Berlin, 2002)

    2002

  37. [45]

    Kubo, Statistical-mechanical theory of irreversible processes

    R. Kubo, Statistical-mechanical theory of irreversible processes. i. general theory and simple applications to magnetic and conduction problems, Journal of the Physical Society of Japan 12, 570 (1957)

    1957

  38. [46]

    Ptaszy´ nski and M

    K. Ptaszy´ nski and M. Esposito, Thermodynamics of quantum information flows, Physical review letters122, 150603 (2019)

    2019

  39. [47]

    McCauley, B

    G. McCauley, B. Cruikshank, D. I. Bondar, and K. Jacobs, Accurate lindblad-form master equation for weakly damped quantum systems across all regimes, npj Quantum Information 6, 1 (2020)

    2020

  40. [48]

    Elouard, M

    C. Elouard, M. Richard, and A. Auff` eves, Reversible work extraction in a hybrid opto-mechanical system, New Journal of Physics 17, 055018 (2015)

    2015

  41. [49]

    Rao and M

    R. Rao and M. Esposito, Conservation laws shape dissipation, New Journal of Physics 20, 023007 (2018)

    2018

  42. [50]

    Esposito, Stochastic thermodynamics under coarse graining, Phys

    M. Esposito, Stochastic thermodynamics under coarse graining, Phys. Rev. E 85, 041125 (2012)

    2012

  43. [51]

    A. Redfield, The theory of relaxation processes* *this work was started while the author was at harvard university, and was then partially supported by joint services contract n5ori-76, project order i., in Advances in Magnetic Resonance , Advances in Magnetic and Optical Reso...

    1965

  44. [52]

    Stevens, D

    J. Stevens, D. Szombati, M. Maffei, C. Elouard, R. Assouly, N. Cottet, R. Dassonneville, Q. Ficheux, S. Zeppetzauer, A. Bienfait, A. N. Jordan, A. Auff` eves, and B. Huard, Energetics of a single qubit gate, Phys. Rev. Lett. 129, 110601 (2022)

    2022

  45. [53]

    Perarnau-Llobet, K

    M. Perarnau-Llobet, K. V. Hovhannisyan, M. Huber, P. Skrzypczyk, N. Brunner, and A. Ac ´ ın, Extractable work from correlations, Phys. Rev. X 5, 041011 (2015)

    2015

  46. [54]

    G. M. Andolina, D. Farina, A. Mari, V. Pellegrini, V. Giovannetti, and M. Polini, Charger-mediated energy transfer in exactly solvable models for quantum batteries, Phys. Rev. B 98, 205423 (2018)

    2018

  47. [55]

    Mazzoncini, V

    F. Mazzoncini, V. Cavina, G. M. Andolina, P. A. Erdman, and V. Giovannetti, Optimal control methods for quantum batteries, Phys. Rev. A 107, 032218 (2023). 39

    2023

  48. [56]

    Cavina and M

    V. Cavina and M. Esposito, Non-equilibrium caldeira-leggett model as a paradigm for quantum autonomous engines, draft in preparation (2023)

    2023

  49. [57]

    et al., A single nitrogen-vacancy defect coupled to a nanomechanical oscillator, Nature Physics 7, 879 (2011)

    Arcizet, O., Jacques, V., Siria, A. et al., A single nitrogen-vacancy defect coupled to a nanomechanical oscillator, Nature Physics 7, 879 (2011)

    2011

  50. [58]

    et al., Inducing micromechanical motion by optical excitation of a single quantum dot, Nature Nanotechnology 16, 283 (2021)

    Kettler, J., Vaish, N., de L´ epinay, L.M. et al., Inducing micromechanical motion by optical excitation of a single quantum dot, Nature Nanotechnology 16, 283 (2021)

    2021

  51. [59]

    Enss and S

    C. Enss and S. Hunklinger, Low-Temperature Physics, SpringerLink: Springer e-Books (Springer Berlin Heidelberg, 2005)

    2005

  52. [60]

    A. J. Roncaglia, F. Cerisola, and J. P. Paz, Work measurement as a generalized quantum measurement, Phys. Rev. Lett. 113, 250601 (2014)

    2014

  53. [61]

    G. D. Chiara, A. J. Roncaglia, and J. P. Paz, Measuring work and heat in ultracold quantum gases, New Journal of Physics 17, 035004 (2015)

    2015

  54. [62]

    A. U. Zyuzin and B. Z. Spivak, Langevin description of mesoscopic fluctuations in disordered media, Sov. Phys. JETP 66, 560 (1987)

    1987

  55. [63]

    Soret, K

    A. Soret, K. Le Hur, and E. Akkermans, Fluctuating forces induced by nonequilibrium and coherent light flow, Phys. Rev. Lett. 124, 136803 (2020)

    2020

  56. [64]

    Soret, O

    A. Soret, O. Shpielberg, and E. Akkermans, Uncertainty relations for mesoscopic coherent light, Journal of Statistical Mechanics: Theory and Experiment 2021, 123302 (2021)

    2021

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