{"id":"465b2ae1-2634-481f-8717-4391e030ebc9","arxiv_id":"2412.02921","paper_version":2,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":3,"one_line_summary":"For a collectively coupled three-level atom-cavity system, dark states of the non-Hermitian jump operator form a tunable multi-dimensional DFS, and shortcut Hamiltonians prepare these states with near-unit purity on timescales of order 1/Γc.","lead":"This paper proposes laser-driven protocols to prepare and control a multi-dimensional decoherence-free subspace in a collective atom-cavity system with three-level atoms. It derives fast 'shortcut to adiabaticity' schemes that reach protected pure states roughly a hundred times faster than quench or adiabatic methods.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The no-purity-loss shortcut is exact only in the single-jump effective model; the paper never quantifies when neglected excited-state spontaneous emission is negligible, leaving the headline claim contingent on an unstated strong-cooperativity condition.","rationale":"I checked the main algebraic construction in the effective model: the non-unitary diagonalization, the DFS dimension formula, and the shortcut Hamiltonians are internally consistent as far as the single-jump master equation is concerned. The reader's weakest assumption points to the same place I would: the mapping from the full atom-cavity Hamiltonian to the single-L model in Eqs. (6)–(8) is where the physical claim acquires its strength. The paper explicitly states that spontaneous decay from excited states is neglected, but it does not derive a concrete inequality such as g²/(κγ)≫1 that would make that neglect safe. Because the shortcut's exactness relies on D[L] being the only dissipator and on the cancellation in Appendix E, an additional spontaneous-emission channel would introduce new jump operators whose kernels do not match the DFS of L, and the reported purity and speedup would not carry over. This is not an internal contradiction, but it is a genuine domain-of-validity gap in the headline claim. The proposed check—repeating the elimination with γ included and comparing final purity across γ_eff/Γc—would settle whether the concern lands. Since the reader already recommended CONDITIONAL for essentially this reason, my read does not change the verdict.","tokens_in":28567,"tokens_out":29609,"duration_ms":305801,"concrete_test":"Re-do the adiabatic elimination of Appendix A with an excited-state decay rate γ included, i.e. add Σ_i D[√γ |g_i⟩⟨e_i|] to the full master equation before eliminating |e_i⟩, and extract the effective ground-state Lindblad operators. Then simulate the shortcut of Sec. V C for N=5, tf=1/Γc, with the same μ(t) and cutoff, for γ_eff/Γc = 0, 0.01, 0.1, and 1 (or for the 87Rb parameters of Ref. [44]). If P(tf) or F(1,tf) drops materially below the reported 0.999/0.99 values at any non-negligible γ_eff/Γc, the no-purity-loss claim is not valid outside the strong-cooperativity limit and should be stated as such.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim—unitary shortcut preparation with P≈1 and tf=1/Γc—is proven only inside the effective master equation (6) with a single jump operator (7). The load-bearing assumption is that the elimination in Appendix A actually leaves this as the only dissipator. In particular, the derivation begins with \"spontaneous decay from the excited states is negligible\" (Appendix A), but the paper never states the quantitative condition under which this is true. Including a spontaneous-emission rate γ from |i_e⟩ produces additional Lindblad terms after eliminating the excited states; once present, the kernel of L is not the protected subspace, and the H_s constructed in Appendix E—which cancels exactly only because D[L] is the sole dissipator—cannot restore purity. Estimating the Raman-scattering rate as γ_eff ∼ γ(Ω/Δ_e)^2 and comparing with Γ_c ∼ κg²Ω²/[Δ_e²(Δ_c'²+κ²)] gives γ_eff/Γ_c ∼ κγ/g² for Δ_c'∼κ, so the required suppression is the single-atom cooperativity g²/(κγ)≫1. The abstract's unqualified \"without any loss of purity\" is therefore contingent on a strong-cooperativity condition that is neither derived nor checked against the 87Rb parameters referenced in the text.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper studies N three-level atoms collectively coupled to a single cavity mode and derives an effective master equation with one jump operator L = √Γc(J_− + μ²J_+ + χ). Through a non-unitary diagonalization of L, the authors classify the decoherence-free subspaces by an integer C = χ/(√2μ), derive the dimension formula D(N,C)=⌈(N+1−|C|)/2⌉, and extract the structure of the dark states. They then compare three preparation protocols for the edge DFS H^{(−N)}_{DFS} and the central DFS H^{(0)}_{DFS}: an instantaneous quench, an adiabatic ramp, and two transitionless shortcuts to adiabaticity implemented by a modified cavity drive or by additional lasers. For N=5, numerical simulations report that the shortcut prepares |ψ_{N,0,0}⟩ with P=0.999992 and F=0.9996 in a time tf=1/Γc, whereas the quench and ramp require hundreds of 1/Γc to reach the 0.99 thresholds. The paper also defines effective Pauli operators that act on two-dimensional DFSs at μ=1.","tokens_in":28804,"tokens_out":19335,"duration_ms":203934,"significance":"If the effective single-jump model is justified, the paper makes a valuable contribution: it gives an explicit analytic diagonalization of a non-Hermitian collective jump operator, a closed-form DFS dimension formula, and shortcut Hamiltonians that are derived from the counterdiabatic condition rather than fitted. These are concrete, reproducible results, and the numerical simulations act as consistency checks on the analytic construction. The paper also identifies entangled dark states with Heisenberg-limit quantum Fisher information, which is a useful observation. The main gap is that the validity domain of the effective model, in particular the neglect of excited-state spontaneous emission, is stated only qualitatively, and the headline claim of purity-preserving preparation is therefore contingent on an unquantified strong-cooperativity condition.","major_comments":[{"comment":"The single-jump effective master equation (6) is the foundation for the DFS and shortcut claims, and its derivation in Appendix A begins with the assumption that spontaneous decay from the excited states is negligible, but no quantitative condition is given. If an excited-state decay rate γ is included, elimination of the excited states produces additional Lindblad operators; the kernel of the single L in Eq. (7) is then no longer the protected subspace, and the shortcut condition (36) cannot guarantee purity. For the detuning regime used in the simulations (Δ′c/κ ≈ 0.1), estimating the effective Raman scattering rate as γ_eff ∼ γ(Ω/Δ_e)^2 and comparing it with Γ_c ∼ κg²Ω²/[Δ_e²(Δ_c′²+κ²)] gives γ_eff/Γ_c ∼ κγ/g², i.e., the single-jump model requires single-atom cooperativity g²/(κγ) ≫ 1. This condition should be derived and checked against the 87Rb parameters referenced in Refs. [44,45]; without it, the abstract's 'without any loss of purity' is contingent on an unstated strong-cooperativity assumption.","section":"Section III and Appendix A"},{"comment":"The statement that the final state for both the quench and the ramp 'must be' |j=N, k3−k1=C⟩ is not literally correct for the quench protocols, because in Tables I and II the quench ends at μ(tf)=μq<1 and the system damps into H^{(C)}_{DFS}(μq), not into H^{(C)}_{DFS}(1). The state |j=N, k3−k1=C⟩ is the unique state in the μ=1 target sector, and the actual quench final state has overlap F(1,tf)≈0.99 rather than exactly 1. The text should either restrict Eq. (43) to the ramp and to the μ=1 component of the quench state, or explain how the j=N conservation plus the C constraint uniquely fixes the quench final state inside H(μq); as written, the claim is inconsistent with the reported fidelities.","section":"Section V D3, Eq. (43)"}],"minor_comments":[{"comment":"The abstract's phrase 'without any loss of purity' is stronger than the implemented protocol: the cavity-drive shortcut uses a cutoff |χ+χs|≤5√2N and the reported values are P=0.999992 and F=0.9996, with the deviation dominated by the cutoff rather than by numerical error. Please qualify the claim as applying to the ideal shortcut in the effective model.","section":"Abstract and Section V C"},{"comment":"The caption says the shortcut has 'unity purity and overlap up to numerical error,' but the F=0.9996 value is limited by the cutoff scheme described in Appendix E 1 and in Section V C; the caption should attribute this small error to the cutoff, not to numerical precision alone.","section":"Table I caption"},{"comment":"The text states that 'it can be proven that we can only shortcut to states that do not possess interparticle entanglement,' but immediately adds that 'the proof does not appear in this work.' Since this restriction is used to select the shortcut targets, please provide a proof, a sketch, or a precise reference; the current statement is an unsupported claim.","section":"Section V C, after Eq. (37)"},{"comment":"The linear independence of the states |ψ_k⟩ in Eq. (23), and hence the claim that they form a basis of the symmetric manifold of dimension (N+2)(N+1)/2, is asserted but not proved. A short argument using invertibility of V in Eq. (18) would make the dimensionality statement self-contained.","section":"Section IV A and Appendix B"},{"comment":"The effective Pauli operators are introduced with the sufficient condition that they commute with L, but the verification is only shown on the two DFS basis states. Please state explicitly that [σ_i,L]=0 holds on the full Hilbert space (or on the full symmetric manifold), since invariance of the DFS under arbitrary superpositions is what guarantees decoherence-free driving.","section":"Section VI, Eq. (47)"}],"recommendation":"major_revision","confidential_remarks":"The formal core of the paper—the non-unitary diagonalization, the DFS dimension formula, and the derived shortcut Hamiltonians—appears sound and is appropriate for PRA. The revision should focus on quantifying the validity of the single-jump effective model and on correcting the quench final-state statement in Sec. V D3; these are fixable within the manuscript's scope, so I do not recommend rejection."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"The genuinely new thing here is the analytic machinery: exact diagonalization of the non-Hermitian jump operator for the three-level collective model, the DFS dimension formula D(N,C), closed-form dark states, and two shortcut Hamiltonians, one of which uses only the existing cavity drive. The derivation is careful, and the numerics are consistency checks on analytic predictions rather than fitted results. The effective Pauli operators for a protected qubit are a useful addition.\n\nThe main soft spot is the unquantified adiabatic elimination. The single-jump master equation assumes spontaneous emission from excited states is negligible, but the paper never states when that is true. Adding a decay rate γ from |i_e> produces extra Lindblad terms, and the kernel of L is no longer the DFS. A quick estimate gives γ_eff/Γ_c ~ κγ/g^2, so the claim requires single-atom cooperativity g^2/(κγ) ≫ 1. That condition is neither derived nor checked against the 87Rb parameters mentioned. The abstract's 'without any loss of purity' is therefore only true inside the model, and should be qualified.\n\nSecond, the restriction to quadratic shortcuts is asserted with 'the proof does not appear in this work.' That is an explicit gap. The authors should either provide the proof or state it as a conjecture.\n\nThird, the numerical comparisons involve hand-set parameters (μ_q, β, the cutoff coefficient in |χ+χ_s| ≤ 5√2N) with no code or data. Given that the analytic results are the point, this is a minor reproducibility issue, but worth addressing.\n\nNone of this invalidates the central construction. The dimension formula, the eigenstates, and the shortcut Hamiltonians are internally consistent, and the paper is honest about the cutoff's effect in Table I. The citation pattern is appropriate; the reuse of Ref. [27] is an extension, not a reframing.\n\nWho this is for: people working on cavity-QED state preparation, decoherence-free subspaces, shortcuts to adiabaticity, or ensemble quantum sensing. It deserves a serious referee. With the strong-cooperativity condition stated, the quadratic-shortcut claim either proved or marked as a conjecture, and the abstract toned down, it would be a solid PRA paper.","headline":"Useful analytic DFS construction for the SU(3) atom-cavity model, but the 'no purity loss' claim needs the strong-cooperativity condition stated; worth refereeing with revisions.","tokens_in":29383,"tokens_out":2362,"would_cite":true,"duration_ms":25638,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":["03.65.Yz","42.50.Pq","03.67.-a"],"model":"deepseek-v4-flash","headline":"Collective atom-cavity dissipation can be engineered into a tunable, multi-dimensional decoherence-free subspace, with shortcut driving preparing pure states in times far shorter than standard adiabatic or dissipative preparation.","keywords":["decoherence-free subspace","collective atom-cavity interactions","non-Hermitian jump operator","adiabatic shortcuts","three-level atoms","dissipative state preparation","effective Pauli operators","quantum metrology"],"falsifier":"Numerically simulate the shortcut protocol for $|\\psi_{N,0,0}\\rangle$ with $N=5$ in the full model that keeps the excited states, adding a spontaneous-emission jump operator at rate $\\gamma$ from each excited state, and scan $\\gamma/\\Gamma_c$ from 0.01 upward while holding all other parameters at the values used in Table I. If the final purity $P(t_f)$ or the target overlap $F(1,t_f)$ falls below 0.99 at a $\\gamma$ small enough that the excited-state elimination should still be valid, the single-jump-operator shortcut is falsified; the same quantity can be checked experimentally by state tomography after a $1/\\Gamma_c$ ramp and by looking for population in the DFS's orthogonal complement.","tokens_in":28330,"feed_emoji":"⚛️","tokens_out":10372,"duration_ms":97998,"temperature":0.7,"pith_summary":"This paper argues that a dissipative atom-cavity system — $N$ three-level atoms collectively coupled to a lossy cavity and driven by tunable lasers — can be reduced, after eliminating the excited states and the cavity, to an effective master equation with a single collective jump operator $\\hat{L}=\\sqrt{\\Gamma_c}(\\hat{J}_-+\\mu^2\\hat{J}_++\\chi)$, and that the kernel of this operator is a decoherence-free subspace whose dimension and orientation can be tuned in time. The paper derives the full structure of every such subspace analytically, shows that typical states inside them are highly entangled, and constructs transitionless shortcut Hamiltonians that keep the system in the instantaneous DFS at all times. The shortcuts prepare pure states in $t_f=1/\\Gamma_c$, compared with $137/\\Gamma_c$ for an adiabatic ramp and $318/\\Gamma_c$ for a dissipative quench (for the edge DFS at $N=5$), with purity and fidelity above $0.9995$. If correct, this provides a fast, experimentally grounded route to protected state preparation and to a logical qubit whose gates commute with the dominant dissipation.","feed_headline":"Decoherence-free states prepared 100x faster by laser shortcuts","feed_subtitle":"Three-level atoms in a cavity keep a tunable protected subspace; shortcut driving reaches 0.9996 fidelity in one cavity lifetime.","key_machinery":"The load-bearing object is the exact diagonalization of the non-Hermitian jump operator $\\hat{L}$ through $L=VDV^{-1}$, which defines two non-canonical sets of Schwinger-boson operators $\\vec{c}=V^\\dagger\\vec{b}$ and $\\vec{d}=V^{-1}\\vec{b}$ and turns $\\hat{L}$ into $\\sqrt{\\Gamma_c}(\\vec{c}^\\dagger D\\vec{d}+\\chi)$. Because $\\hat{L}$ is not Hermitian unless $\\mu=1$, the eigenstates and the complementary space are built from $\\hat{c}^\\dagger$ and $\\hat{d}^\\dagger$ respectively; their biorthogonal overlap $\\langle\\psi^\\perp_{\\vec{n}}|\\psi_{\\vec{k}}\\rangle\\propto \\delta_{\\vec{n}\\vec{k}}$ is what makes the complementary subspace analytically tractable. This diagonalization reduces the search for a DFS to a counting problem on the integer $C=k_3-k_1$ and gives the explicit dimension formula, and it provides the matrix elements $\\langle\\psi^\\perp_{\\vec{n}}|\\partial_t\\psi_{\\vec{k}}\\rangle$ that the shortcut Hamiltonians must match. The two shortcut mechanisms are the cavity-drive modification $\\chi\\to\\chi+\\chi_s$ for the edge DFSs and an additional laser coupling between the $|-1_g\\rangle$ and $|1_g\\rangle$ states for the central DFS; both are quadratic in single-particle operators and therefore reach only unentangled target states.","core_discovery":"At the center of the paper is the observation that the single non-Hermitian jump operator $\\hat{L}=\\sqrt{\\Gamma_c}(\\hat{J}_-+\\mu^2\\hat{J}_++\\chi)$ can be diagonalized exactly by a non-unitary transformation in Schwinger-boson space, $\\hat{L}=\\sqrt{\\Gamma_c}[\\sqrt{2}\\mu(\\hat{c}_1^\\dagger\\hat{d}_1-\\hat{c}_3^\\dagger\\hat{d}_3)+\\chi]$. Its eigenstates are $|\\psi_{\\vec{k}}\\rangle\\propto(\\hat{c}_1^\\dagger)^{k_1}(\\hat{c}_2^\\dagger)^{k_2}(\\hat{c}_3^\\dagger)^{k_3}|0\\rangle$ with eigenvalues $\\sqrt{\\Gamma_c}[\\sqrt{2}\\mu(k_1-k_3)+\\chi]$, so the DFS is exactly the span of all eigenstates with $k_3-k_1=C=\\chi/(\\sqrt{2}\\mu)$, a subspace of dimension $\\lceil(N+1-|C|)/2\\rceil$ whose states move as $\\mu$ and $\\chi$ are ramped. The paper then constructs shortcut Hamiltonians satisfying $\\langle\\psi^\\perp_{\\vec{n}}|\\hat{H}_s|\\psi_{\\vec{k}}\\rangle=i\\hbar\\langle\\psi^\\perp_{\\vec{n}}|\\partial_t\\psi_{\\vec{k}}\\rangle$ to cancel all leakage into the complementary subspace; this yields the numerically demonstrated preparation of $|\\psi_{N,0,0}\\rangle$ and $|\\psi_{0,N,0}\\rangle$ in $t_f=1/\\Gamma_c$. At $\\mu=1$ the jump operator becomes Hermitian and the DFS hosts effective Pauli operators $\\hat{\\sigma}_x,\\hat{\\sigma}_y,\\hat{\\sigma}_z$ that drive a protected qubit while commuting with $\\hat{L}$.","pith_inferences":["The shortcut Hamiltonians are quadratic in single-particle operators, so they can only reach unentangled product states; combining that with the paper's commuting Pauli operators suggests a two-stage recipe — shortcut to $|\\psi_{0,N,0}\\rangle$, then drive inside the DFS — for preparing the highly entangled, metrologically useful states, a concatenation the paper leaves implicit.","Because the edge-DFS shortcut requires $\\chi_s\\propto(\\mu^4-1)^{-1}$, the 'not limited by any error rate' claim is in practice bounded by available laser power near $\\mu=1$; a natural extension would be to optimize the pulse shape $\\mu(t)$ or splice the two shortcut types to minimize peak power for a fixed total time.","If spontaneous emission is added perturbatively, it introduces jump operators that do not share the kernel of $\\hat{L}$; computing the resulting leakage in first-order perturbation theory would give a quantitative bound on when the DFS protection degrades, which the paper does not provide.","The effective Pauli operators require four-operator (two-atom) interaction terms, so realizing the protected qubit gates will require a physical mechanism beyond the single-particle drives used for the shortcuts; identifying such a mechanism and testing gate fidelities under the same parameter hierarchy is a direct next step."],"forward_implications":["A pure target state can be prepared in a time $t_f=1/\\Gamma_c$, roughly two orders of magnitude faster than the best adiabatic ramp ($137/\\Gamma_c$) or quench ($318/\\Gamma_c$) reported for the same $N=5$ system, so the state spends far less time exposed to noise the DFS does not protect against.","The DFS dimension can be dialed from 1 to $\\lceil(N+1)/2\\rceil$ by choosing the integer $C=\\chi/(\\sqrt{2}\\mu)$, so a single setup can store a protected qubit, a qutrit, or a higher-dimensional qudit without changing the apparatus.","Because all states in the DFS are simultaneous eigenstates of $\\hat{L}$, any operator that commutes with $\\hat{L}$ (such as the effective Pauli operators of Sec. VI) can implement gates inside the subspace without causing decoherence; the qubit is therefore naturally robust against single-particle errors.","The DFS contains states with quantum Fisher information scaling as $N^2/2+N$ at $\\mu=1$, so the protected subspace doubles as a source of Heisenberg-limited metrological sensitivity.","The shortcut to the central DFS state $|\\psi_{0,N,0}\\rangle$ is exact in simulation ($P=F=1$ up to numerical error), while the edge shortcuts carry only a small cutoff-induced error ($P=0.999992$, $F=0.9996$), meaning the main practical limitation is laser power near $\\mu=1$, not the shortcut principle itself."],"supporting_citations":[{"why":"Supplies the transitionless shortcut condition $\\langle\\psi^\\perp|\\hat{H}_s|\\psi\\rangle=i\\hbar\\langle\\psi^\\perp|\\partial_t\\psi\\rangle$ used to construct the shortcut Hamiltonians.","marker":"[24]"},{"why":"Provides the adiabatic-control-of-DFS methodology and the collective atom-cavity model with a jump operator structure that this paper extends to three levels and exact non-unitary diagonalization.","marker":"[27]"},{"why":"Gives the Lidar-Chuang-Whaley criterion that DFS basis states must be degenerate eigenstates of all jump operators, which defines the DFS here.","marker":"[33]"},{"why":"Supplies the dynamic-stability criteria for DFSs, including the effective-Hamiltonian invariance condition the paper checks.","marker":"[25]"},{"why":"Provides the dissipative steady-state preparation approach (damping into a DFS) used as the quench baseline for comparison.","marker":"[37]"},{"why":"Reports the experimental realization of the spin-1 Dicke model in 87Rb with cavity-assisted Raman transitions, grounding the level scheme and drive configuration.","marker":"[44]"},{"why":"Supplies the quantum Fisher information entanglement witness used to show that certain DFS states have Heisenberg-limit metrological sensitivity.","marker":"[53]"},{"why":"Provides the method for eliminating dissipative bosonic modes to obtain the effective Lindblad master equation with a single jump operator.","marker":"[75]"},{"why":"Reviews shortcuts to adiabaticity and frames the shortcut approach the paper adapts to the DFS setting.","marker":"[46]"}],"fun_headline_variants":["Laser shortcuts steer atoms into tunable decoherence-free states","Tunable decoherence-free subspaces realized with laser-driven shortcuts","Protected qubit in a cavity via tunable decoherence-free subspace","Adiabatic shortcuts prepare entangled DFS states with high fidelity","Laser shortcuts create tunable multi-dimensional decoherence-free subspaces"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The entire construction rests on the assumption that the fast degrees of freedom (cavity photons and excited atomic states) can be eliminated so that exactly one dissipation channel remains, described by the single jump operator $\\hat{L}$; if spontaneous emission from the excited states is not negligible, or if the detuning and timescale hierarchies $\\Delta_e\\gg g,|\\Omega_i|$, $g\\gg|\\Omega_i|$, $\\kappa\\gg|\\sqrt{N}g\\Omega_i/\\Delta_e|$, $\\kappa\\gg \\partial_t\\eta/\\eta,\\partial_t\\Omega_i/\\Omega_i$ are violated, additional jump operators appear and the kernel of $\\hat{L}$ is no longer the protected subspace.","fun_headline_variants_meta":{"raw":{"variants":["Laser shortcuts steer atoms into tunable decoherence-free states","Tunable decoherence-free subspaces realized with laser-driven shortcuts","Protected qubit in a cavity via tunable decoherence-free subspace","Adiabatic shortcuts prepare entangled DFS states with high fidelity","Laser shortcuts create tunable multi-dimensional decoherence-free subspaces"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000863,"raw_usage":{"total_tokens":3800,"prompt_tokens":1057,"completion_tokens":2743,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":673,"completion_tokens_details":{"reasoning_tokens":2651}},"tokens_in":673,"tokens_out":2743,"duration_ms":19887,"temperature":1.0,"reasoning_tokens":2651,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-11T22:58:57.434965+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Numerically simulate the shortcut protocol for $|\\psi_{N,0,0}\\rangle$ with $N=5$ in the full model that keeps the excited states, adding a spontaneous-emission jump operator at rate $\\gamma$ from each excited state, and scan $\\gamma/\\Gamma_c$ from 0.01 upward while holding all other parameters at the values used in Table I. If the final purity $P(t_f)$ or the target overlap $F(1,t_f)$ falls below 0.99 at a $\\gamma$ small enough that the excited-state elimination should still be valid, the single-jump-operator shortcut is falsified; the same quantity can be checked experimentally by state tomography after a $1/\\Gamma_c$ ramp and by looking for population in the DFS's orthogonal complement.","supporting_citations":[{"cited_title":"We may apply this additional Hamiltonian in concert with the original ˆHat in order to drive directly from the initial state |ψ(0)⟩ into the target state","cited_arxiv_id":null,"evidence_quote":"Supplies the transitionless shortcut condition $\\langle\\psi^\\perp|\\hat{H}_s|\\psi\\rangle=i\\hbar\\langle\\psi^\\perp|\\partial_t\\psi\\rangle$ used to construct the shortcut Hamiltonians."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Supplies the quantum Fisher information entanglement witness used to show that certain DFS states have Heisenberg-limit metrological sensitivity."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Provides the method for eliminating dissipative bosonic modes to obtain the effective Lindblad master equation with a single jump operator."}],"review_version":1}