{"id":"f4e0dd66-9901-4873-bff6-03eb54b6d488","arxiv_id":"2607.25176","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":7.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":0,"one_line_summary":"Relaxation during pulsed dynamical decoupling makes interference visibility grow linearly with detuning and flips the interference phase by π at resonance, as shown in strontium atoms and a transmon.","lead":"Excited-state decay during a Carr-Purcell pulse train turns the usual detuning suppression of dynamical decoupling into a strong detuning-dependent interference signal. The same effect appears in a strontium atom interferometer and a superconducting transmon, and it is used to build a new spectroscopy method.","discovery_kind":"first_principles","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The exact prefactor in Eq. (4) and the DCPS transfer function Eq. (8) rest on an unverified assumption that decay events are uniformly distributed over each two-pulse cycle; the paper does not show that a full optical-Bloch-equation treatment with instantaneous decay rate proportional to p_e(t) repr","rationale":"The paper's central claim is the quantitative prediction Eq. (4): in a CP sequence much longer than T1, excited-state decay makes the visibility grow linearly as v=(2T+tau_pi)/(T+tau_pi)|delta/Omega| and makes the phase flip by pi. This formula, and the derived DCPS transfer function Eq. (8), come from averaging over decay times as if the decay rate were gamma/2 everywhere (Appendix A and B). The reader correctly identified this as the weakest assumption. The paper gives parameter-free analytics and observes the qualitative V-shape and phase flip in two independent platforms, which is real support; it also uses OBE simulations for related quantities. However, the explicit comparison to Eq. (4) is qualitative, and the simulations used for the Bloch-sphere visualization sample decay times uniformly rather than solving the full master equation. The uniform weighting is plausible at delta=0 because the two pulses in a cycle have complementary excited-state population dynamics, but the paper does not demonstrate that this complementarity survives to first order in delta or that it preserves the exact prefactor. A controlled Lindblad simulation is the direct check: it removes the uniform-time approximation and tests both the central visibility formula and the DCPS noise-filtering claim. This does not overturn the reader's conditional verdict; it identifies the specific quantitative step that needs confirmation. No stronger objection, such as a logical inconsistency or a clear falsification by the data, was found.","tokens_in":30416,"tokens_out":18953,"duration_ms":201143,"concrete_test":"Run a Lindblad master-equation simulation of the exact CP sequence used in Fig. 3 (Hamiltonian of Eq. A1 plus sigma_- jump with rate gamma, no uniform-time sampling) for the Sr parameters (T=tau_pi=112 ns, T1=21.3 micro-s, 504 pi pulses) and for the transmon parameters (T=tau_pi=300 ns, T1=21 micro-s, 200 pi pulses). For delta/Omega in [-0.04, 0.04], compute <p1> as a function of readout phase phi_R, fit to <p1>=1/2(1+v cos(Delta phi + phi_R))+b, and compare the small-delta slope of v versus Eq. (4) and the phase jump at delta=0. Separately inject a single frequency-noise tone into the same master equation and compare the r.m.s. detuning error to the Lorentzian sqrt(3)gamma linewidth of Eq. (8). If the master-equation slope differs from (2T+tau_pi)/(T+tau_pi) by more than 10%, or the linewidth differs from sqrt(3)gamma, the uniform-weighting assumption fails and the quantitative central","verdict_should_be":"UNCHANGED","load_bearing_attack":"The analytical core (Appendix A, Eqs. A13-A14, and Appendix B, Eq. B10) replaces the true decay-time distribution with a uniform average over each two-pulse cycle, i.e. it takes the instantaneous decay rate to be gamma/2 at all times. The central formula Eq. (4) - linear visibility growth and pi phase flip - and the DCPS transfer function Eq. (8) both inherit this assumption. For a coherently driven CP sequence this is not obviously valid: during each pi pulse the excited-state population oscillates (for one pulse of a cycle p_e(t)=(1+sin Omega t)/2, for the other approximately the complement), so the probability density of a decay event is not flat in time. At delta=0 the two pulses of a cycle may combine to give a uniform distribution, but for delta != 0 the states before the two pulses are no longer exactly opposite. An O(delta) modulation of the decay-time distribution can multiply the O(1) oscillatory terms in p1(tau) and produce an O(delta) correction to the coefficient in Eq. (4). The paper reports only qualitative agreement and does not show that a full optical-Bloch-equation treatment, with decay rate proportional to instantaneous p_e, reproduces the specific prefactor (2T+tau_pi)/(T+tau_pi) or the sqrt(3)gamma DCPS linewidth. Since Eq. (4) is the quantitative foundation for the claimed dissipation-enabled detuning dependence and for DCPS, this unverified weighting assumption is the most load-bearing soft spot.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"This paper claims that excited-state decay in a Carr-Purcell (CP) dynamical-decoupling sequence, in the limit where the sequence is much longer than T1, converts the usual detuning insensitivity of DD into a strong detuning-dependent interference signal. The central analytic result, Eq. (4), predicts a visibility v=(2T+τπ)/(T+τπ)|δ/Ω| and a π phase jump at zero detuning. The derivation in Appendix A is a gate-based average over possible decay times within a two-pulse cycle. The same mechanism is used to introduce Dissipative Carr-Purcell Spectroscopy (DCPS), with a Lorentzian noise transfer function H(ω)=√(γ²/[2(γ²+4ω²)]) derived in Appendix B. The effect is demonstrated experimentally in a ⁸⁸Sr atom interferometer and a superconducting transmon qubit, with qualitative agreement to the analytic lines and to optical-Bloch-equation simulations.","tokens_in":30846,"tokens_out":32117,"duration_ms":282603,"significance":"If the central claims hold, the paper establishes a conceptually new regime of pulsed dynamical decoupling in which dissipation does not merely degrade coherent control but creates a new, strong detuning sensitivity. The two-platform experimental demonstration (Sr atom interferometer and transmon) is a significant strength, as is the absence of fitted parameters: the theory lines in Fig. 3 use only independently set pulse parameters and measured T1. The proposed DCPS technique, with its predicted √3γ linewidth and high-frequency noise suppression, is a potentially useful complement to Ramsey spectroscopy in specific regimes. The paper is clearly written, with detailed appendices and a transparent disclosure of generative-AI assistance. The main weakness is that the analytical core rests on an unstated uniform-decay-time weighting whose quantitative accuracy is not directly validated by a full optical-Bloch-equation simulation without inhomogeneous broadening.","major_comments":[{"comment":"The average over decay times in Eqs. (A13)-(A14) weights each interval of the two-pulse cycle by its duration, i.e. it assumes a uniform distribution of decay events within the cycle. The instantaneous decay rate is γp_e(t), and p_e(t) oscillates within each pulse and acquires an O(δ) component when the pulse rotation axis tilts. The paper does not explicitly show that the resulting correction to the coefficient in Eq. (4) is higher order in the stated small parameter 2(T+τπ)≪1/γ. A direct quantitative check is missing: Fig. 3 shows only analytic lines and data, not the corresponding OBE simulation without inhomogeneous broadening. Please add either an explicit order-counting argument or a comparison of Eq. (4) with a full Lindblad/OBE simulation for the same T, τπ, Ω (and no detuning spread), showing that the prefactor (2T+τπ)/(T+τπ) is reproduced.","section":"§II A and Appendix A, Eqs. (A13)-(A14), Eq. (4)"},{"comment":"The DCPS transfer function Eq. (8) and the √3γ linewidth inherit the same uniform-decay-time assumption via Eq. (B10). The text states that simulations reproduce the √3γ FWHM, but no overlay of the full simulation with Eq. (8) is shown, so it is not verified that the absolute scale of H (used in Eq. (9) to convert a measured noise spectrum into a detuning error) is reproduced. Furthermore, the correction factor B in Eq. (B18) is defined by matching the smoothed integral to the exact integral within the uniform-decay model; it does not address the weighting issue. Please provide a direct comparison of the simulated transfer function (both FWHM and amplitude) with Eq. (8).","section":"§III and Appendix B, Eqs. (B10)-(B18), Eq. (8)"}],"minor_comments":[{"comment":"The phase expression Δφ=π+(−π/2 for δ>0, π/2 for δ<0) is equivalent to Δφ=π/2 for δ>0 and 3π/2 for δ<0 modulo 2π. This is correct but somewhat opaque; stating the two values explicitly would help readers connect to the π-flip claim.","section":"Eq. (4)"},{"comment":"The sentence 'This result captures only the leading-order effect … which are expected to further reduce the measured visibility beyond what Eq. (4) predicts' is confusing at δ=0, where Eq. (4) gives zero visibility and additional loss cannot reduce it further. The nonzero visibility observed at δ=0 in Fig. 3 should be discussed explicitly (e.g., residual detuning spread or O(δ²) effects).","section":"§II A, text near Fig. 3"},{"comment":"The horizontal axis of the left panel is labelled as γ but does not show units; for clarity, specify that it is the relaxation rate in s⁻¹. The right panel horizontal axis is T_seq/T1, which is fine, but the y-axis label is truncated and should read '∂Δφ/∂(δ/Ω)'.","section":"Fig. 8"},{"comment":"There is a typo: 'the the detuning senstivity' should be 'the detuning sensitivity'.","section":"§II A, near Fig. 9"},{"comment":"The main text should state explicitly that Eq. (4) is derived to first order in δ and to leading order in the small parameter γ(T+τπ). This would preempt the concern about uniform decay-time weighting and make the domain of validity of the formula clear.","section":"Appendix A"}],"recommendation":"major_revision","confidential_remarks":"The stress-test concern about the uniform decay-time weighting is real but, in my reading, likely leads to corrections of order γ(T+τπ) δ/Ω, which are small in the stated parameter regime. The paper would still benefit from an explicit statement and a clean simulation check. The missing OBE comparison for Eq. (4) is the most important technical gap; it can be fixed without changing the overall claims. The manuscript is within the scope of the journal and, after the requested revisions, should be publishable."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Two things to know about this one. The central effect is real and well-supported: for a Carr–Purcell sequence much longer than T1, excited-state decay alone produces an interference visibility that grows linearly with |δ/Ω| and a phase that jumps by π through zero. They derive it from first principles, no fitted parameters, and they see the same V-shape and phase flip in a 88Sr interferometer and a transmon. That is worth a careful look.\n\nWhat is genuinely new: previous treatments of DD and detuning assume the standard suppression; this says relaxation breaks it in a specific, calculable way. The gate-based picture (Fig. 1) is helpful, and the analytic result is simple enough to check. The DCPS idea is a reasonable spin-off — using that sensitivity as a spectroscopic probe — though it is clearly secondary.\n\nNow the soft spots, in proportion. The analytic model averages decay times uniformly over each two-pulse cycle, i.e., it treats the instantaneous decay rate as γ/2 at all times. That is an approximation. During a π-pulse the excited-state population oscillates, so the true decay-time distribution is not flat; for nonzero δ the two pulses of a cycle are not exact complements, and an O(δ) ripple in the distribution can feed into the O(δ) coefficient of Eq. (4). The stress-test is right that the paper never shows a full optical-Bloch-equation treatment reproduces the specific prefactor (2T+τπ)/(T+τπ) or the √3γ DCPS linewidth. Given the experiments claim only qualitative agreement, this is not fatal, but it does mean the quantitative foundation is unverified.\n\nSecond soft spot: the zero-detuning axis is calibrated by the visibility minimum—which is itself a prediction of the model. That makes the comparison partially circular, even if not deliberately so. A cleaner test would use an independent resonance calibration.\n\nThird, the DCPS transfer-function data sit near the noise floor (Fig. 10). The Ramsey comparison is fine, but the DCPS part is suggestive, not demonstrated. The Allan deviation comparison is honestly inconclusive, as they state.\n\nBottom line: the paper deserves a serious referee, and I would give it one. The core effect is important for quantum control and metrology, the derivation is transparent, and the two-platform evidence is strong. The referee should ask for a full OBE check of the prefactor and an independent δ=0 calibration, but these are addressable rather than fatal. I would take it if I worked in this area.","headline":"Dissipation-induced detuning sensitivity in CP sequences is real and shown on two platforms, but the exact prefactor and the DCPS linewidth rest on an unverified uniform-decay weighting.","tokens_in":31297,"tokens_out":3642,"would_cite":true,"duration_ms":35295,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"Excited-state decay makes a Carr-Purcell pulse sequence sharply sensitive to detuning, turning dissipation into a usable spectroscopic signal.","keywords":["dynamical decoupling","Carr-Purcell sequence","excited-state decay","detuning sensitivity","interference visibility","quantum spectroscopy","Bloch sphere","dissipative Carr-Purcell spectroscopy"],"falsifier":"Take a CP sequence with total duration much longer than T1, set the final readout phase to φR = π/2, and measure ⟨p1⟩ as a function of δ/Ω. Eq. (4) predicts a slope of −(2T+τπ)/(2(T+τπ)) at small δ, approaching −3/4 when T = τπ; if the measured slope remains near zero for large sequence durations, or the visibility does not grow as |δ/Ω|, the uniform-decay-time model is invalidated.","tokens_in":30359,"feed_emoji":"⚛️","tokens_out":4333,"duration_ms":45853,"temperature":0.7,"pith_summary":"This paper argues that dissipation, in the form of excited-state decay, can change the defining behavior of pulsed dynamical decoupling: instead of suppressing sensitivity to detuning errors, a Carr-Purcell sequence whose duration exceeds the qubit lifetime acquires a strong, predictable detuning dependence. The mechanism is that a decay event resets the qubit to the ground state, and the partial pulse following the reset acts as a π/2-like rotation that starts a new superposition whose phase is no longer fully compensated by subsequent pulses. The paper predicts, to first order in the detuning δ, that the final interference visibility grows linearly with the normalized detuning |δ/Ω| and that the phase shift flips by π as δ crosses zero. This effect is reproduced analytically, in optical-Bloch-equation simulations, and in experiments on both a strontium atom interferometer and a superconducting transmon qubit. The authors use the effect as the basis for a new spectroscopic technique, Dissipative Carr-Purcell Spectroscopy (DCPS), which suppresses high-frequency frequency noise while retaining sensitivity to a static detuning offset.","feed_headline":"Decay makes long Carr-Purcell pulses linearly sensitive to detuning","feed_subtitle":"Relaxation turns a decoupling sequence into a detuning sensor with a π phase jump, observed in atoms and transmons.","key_machinery":"The central object is the Carr-Purcell two-pulse cycle — one X gate plus free evolution repeated with opposite phase — which, to first order in the detuning, acts as a global phase (X U_F^T X U_F^T ≈ −1 + O(δ²)). This makes the final state depend only on where in the cycle a decay event occurs, and averaging the four possible decay locations (pulse vs deadtime, even vs odd number of subsequent X gates) with durations weighted by their share of the cycle produces Eq. (4). The partial X gate immediately following a decay acts as a π/2-like rotation, creating the coherence that then accumulates detuning-dependent phase over the remaining pulses.","core_discovery":"For a Carr-Purcell (CP) sequence of repeated X gates with free-evolution intervals T and π-pulse duration τπ, in the limit that the total sequence duration is much longer than the excited-state lifetime T1, the ensemble-averaged excited-state population is, to first order in the detuning δ, ⟨p1⟩ = 1/2 − (2T+τπ)/(2(T+τπ)) (δ/Ω) sin φR. Writing this as a fringe gives a visibility v = (2T+τπ)/(T+τπ) |δ/Ω| and a phase Δφ = π ∓ π/2 for δ > 0 and δ < 0, respectively. The mechanism is that a qubit which decays during the sequence is reset to |0⟩ and then experiences only the remaining pulses; depending on where in the two-pulse cycle the decay occurs, the subsequent evolution leaves a detuning-depe","pith_inferences":["The same mechanism should apply to any incoherent reset channel that leaves the qubit in |0⟩, not only T1 decay — for example, measurement-induced reset or repumping errors — so similar detuning fringes might be observed in other driven quantum systems.","Because the visibility grows linearly with detuning and the phase flips sign, the effect could be used as a sensitive, calibration-free null detector for drive detuning in experimental setups, complementing Ramsey spectroscopy in regimes with short T2* but long T1.","When extending DD sequences beyond T1 for quantum-lock-in sensing or error suppression, residual detuning sensitivity caused by relaxation may need to be included in error budgets, even if the individual pulses are perfect.","In multi-photon driven systems where relaxation occurs only during the pulses, the uniform-time-weighting analysis would break down; the effect might then depend on pulse duty cycle in a different way, offering a test of the underlying assumption."],"forward_implications":["Increasing the total duration of a CP sequence relative to T1 strengthens the relaxation-induced detuning sensitivity, as shown by a measured slope that grows toward the predicted asymptotic value of 3/4 for ∂⟨p1⟩/∂(δ/Ω).","The same effect appears in two very different physical systems (a free-space atom interferometer and a superconducting transmon), suggesting it is a generic feature of driven two-level systems with relaxation.","DCPS yields a frequency-noise transfer function of the form H(ω) ∝ √(γ²/(γ² + 4ω²)), with a linewidth of √3 γ, so it rejects noise above the relaxation rate while retaining sensitivity to a static detuning.","Not all dynamically decoupling sequences are equally affected: CP is the most relaxation-sensitive, while XY-8 and UR-8 remain comparatively robust, which matters for choosing a sequence when phase precision is required.","At zero detuning the CP-sequence visibility vanishes (the arcs of decayed qubits cancel), whereas an alternating-phase −Y,Y sequence produces a large relaxation-induced coherence at δ=0, showing that dissipation′s effect depends sensitively on pulse phases."],"fun_headline_variants":["Decay flips Carr-Purcell pulses into detuning sensors","Relaxation turns decoupling into a detuning probe","Dissipation reshapes decoupling into a sensitive interferometer","Decay-induced interference for detuning metrology in qubits","How decay turns a decoupling sequence into a spectroscopy tool"],"cache_read_input_tokens":2304,"weakest_assumption_plain":"The calculation assumes that the two-pulse cycle is much shorter than T1 and that the excited-state population remains near one-half throughout the sequence, so decay events can be averaged uniformly over pulse and dead-time intervals; if pulses significantly modulate the population within a cycle, the linear visibility law and the π phase jump need not hold.","fun_headline_variants_meta":{"raw":{"variants":["Decay flips Carr-Purcell pulses into detuning sensors","Relaxation turns decoupling into a detuning probe","Dissipation reshapes decoupling into a sensitive interferometer","Decay-induced interference for detuning metrology in qubits","How decay turns a decoupling sequence into a spectroscopy tool"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000219,"raw_usage":{"total_tokens":1298,"prompt_tokens":780,"completion_tokens":518,"prompt_tokens_details":{"cached_tokens":256},"prompt_cache_hit_tokens":256,"prompt_cache_miss_tokens":524,"completion_tokens_details":{"reasoning_tokens":434}},"tokens_in":524,"tokens_out":518,"duration_ms":5444,"temperature":1.0,"reasoning_tokens":434,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-01T03:13:13.676345+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Take a CP sequence with total duration much longer than T1, set the final readout phase to φR = π/2, and measure ⟨p1⟩ as a function of δ/Ω. Eq. (4) predicts a slope of −(2T+τπ)/(2(T+τπ)) at small δ, approaching −3/4 when T = τπ; if the measured slope remains near zero for large sequence durations, or the visibility does not grow as |δ/Ω|, the uniform-decay-time model is invalidated.","supporting_citations":[],"review_version":1}