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Anomalous supercurrents in the presence of particle losses

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Pith's one-line read Single-particle losses at a quantum dot can reverse a Josephson supercurrent, reverse a dissipation-induced spin supercurrent, and in a narrow regime increase the critical current.

desk verdict A clearly formulated GKSL treatment of a lossy Josephson junction with novel predictions, but the strong-dissipation regime where the anomalies appear sits where the Markovian assumption starts to creak. read the letter →

arxiv 2505.21085 v1 pith:BGZ4YSGM submitted 2025-05-27 cond-mat.quant-gas cond-mat.mes-hallcond-mat.supr-con

Risa Ogino , Shun Uchino This is my paper
classification cond-mat.quant-gascond-mat.mes-hallcond-mat.supr-con
keywords Josephsoneffectpi-junctionquantumdotparticlelossLindbladmasterequationKeldyshformalismspinsupercurrentultracoldatomicgases
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

The paper studies a Josephson junction whose conduction channel is a quantum dot with particle loss, as realized in ultracold-atomic-gas experiments. It claims that the loss does not merely weaken the supercurrent: once the loss rate is comparable to the superconducting gap and the channel is weakly transmitting, the current-phase relation develops a zero between zero and pi and the current reverses sign, forming a pi-junction. In a narrow parameter window, dissipation instead increases the critical current. For spin-selective loss, the paper predicts a spin supercurrent that is entirely generated by dissipation and can also reverse its direction.

What carries the argument

The mechanism is a decomposition of the Keldysh current into conventional and unconventional parts, where the unconventional part is exactly the term generated by the quantum-jump component of the Gorini-Kossakowski-Sudarshan-Lindblad master equation. In the dot's inverse Keldysh Green's function, single-particle loss appears as diag(2 i γ↑, −2 i γ↓); this is what feeds I_N,uc and I_S,uc. A trace identity forces the conventional spin-current contribution I_S,c to vanish, so the spin supercurrent exists only because of the loss term. In the clean limit the formulas reproduce the standard Andreev bound-state current I_ABS with Andreev energy E_ABS = Δ sqrt(1 − T sin²(φ/2)).

What would settle it

In a single-channel lossy junction with Γ/Δ < 1 and transmission around 0.5, plot I_N(φ) as the loss rate γ/Δ is swept from 0 to 2: the prediction is that the current acquires a node in 0 < φ < π and turns negative, while the critical current is non-monotonic with a maximum near γ/Δ = 1; for spin-selective loss, a spin supercurrent with a reversed phase relation should appear. An experiment or exact quantum-trajectory simulation that finds no such node and no non-monotonic critical current would settle the claim negatively.

Watch

Extended reading notes

Core claim

The paper's central claim is that Markovian single-particle loss in the conduction channel of a Josephson junction changes the supercurrent in ways that go beyond simple suppression. Splitting the current into a conventional part I_{N,c} and a loss-induced part I_{N,uc}, the authors find that at weakly transmitting junctions (Γ/Δ < 1) the two contributions have opposite signs, so I_N(φ) acquires a node inside 0 < φ < π and the current reverses direction, giving a pi-junction. In a narrow window around Γ/Δ ≈ 1, the loss-induced part is non-monotonic and can push the critical current above its clean value. For spin-selective loss, the conventional spin current vanishes identically, so the entire spin supercurrent is generated by dissipation and can itself reverse as a function of phase.

Load-bearing premise

The whole prediction rests on the loss at the dot being memory-free and describable by a Lindblad master equation with a non-interacting dot, with both reservoirs remaining in equilibrium; strong interactions or non-Markovian loss could modify or erase the anomalous node, the critical-current enhancement, and the spin supercurrent.

Editorial extensions

If this is right

  • Tuning a loss rate provides a dissipation knob for the current-phase relation, converting a 0-junction into a pi-junction without magnetic fields or ferromagnetic layers.
  • In the weak-tunneling regime the critical current is predicted to grow with the loss rate up to γ/Δ ≈ 1, so moderate dissipation can improve, not merely degrade, superfluid phase coherence.
  • Spin-selective particle loss acts as a switchable source of pure spin supercurrent, with its sign controlled by Γ/Δ and the phase bias.
  • Because the non-dissipative limit reproduces the conventional Andreev bound-state result, the calculation sets a baseline for detecting the predicted anomalous terms in existing lossy point-contact experiments.

Reading between the lines

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

  • The same current-phase anomalies should appear for any environment that yields a Keldysh inverse dot Green's function of the form diag(2 i γ, −2 i γ), so a tunnel-coupled normal drain in a three-terminal superconductor device is a plausible solid-state test of the pi-junction prediction.
  • Adding a Hubbard interaction U to the dot would test how fragile the effect is: as U broadens or shifts the dot spectral function, the node in I_N(φ) should move or disappear, which directly probes whether the non-interacting model is essential.
  • In the spin-selective case, the spin-current reversal implies a dissipation-tunable spin polarization of the reservoirs; measuring the accumulated spin imbalance versus phase bias would test the prediction without requiring direct spin-current read-out.
  • The distinction between the jump term and a non-Hermitian effective Hamiltonian could be tested by recomputing the current with the Keldysh term set to zero: the pi-junction and spin supercurrent should vanish, confirming that full Lindblad dynamics, not just complex energy levels, drive the effect.
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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

1 major / 6 minor

Summary. The manuscript studies a Josephson junction consisting of two superconducting or superfluid reservoirs coupled through a non-interacting quantum dot subject to single-particle losses. Using a Keldysh field-theory formulation of the GKSL master equation, the authors derive current formulas and report that spin-independent losses can produce a supercurrent that vanishes at a phase between 0 and pi and reverses sign (pi-junction), additional nodes in the current-phase relation, and, in a narrow parameter window, a dissipation-enhanced critical current. For spin-selective losses, they find a dissipation-induced spin supercurrent and its reversal. The analytical expressions are checked against the known Andreev limit in Eq. (C4).

Significance. The paper's main strength is a parameter-free (within the model) Keldysh-Dyson calculation with detailed appendices, and the reduction to the standard Andreev current is a useful consistency check. If the predictions survive a more microscopic treatment of the dissipation, the results establish a new route to controlling Josephson junctions via particle losses, with direct relevance to ultracold-atom experiments and three-terminal solid-state setups. The spin-supercurrent result is particularly novel because it includes the quantum-jump contribution of the Lindblad evolution rather than only the non-Hermitian part. The main technical risk is the validity of the Markovian master equation in the parameter regime where the anomalies appear, which the manuscript does not yet address.

major comments (1)
  1. [II (Eq. 5 and Eq. A10), III.A (Fig. 2b, Fig. 5)] The anomalous phenomena are obtained in the regime where both the loss rate and the tunneling-induced broadening are comparable to the superconducting gap: the pi-junction appears at gamma/Delta=1 with Gamma/Delta=0.1 (Fig. 2b), and the critical-current enhancement is found at Gamma/Delta=1 and T=0.1 (Fig. 5). The paper starts from the Lindblad master equation (Eq. 5) and the corresponding Keldysh inverse dot Green's functions (Eq. A10), but it does not state the Born-Markov and weak-coupling conditions under which such a master equation is a controlled microscopic description of single-particle losses. For a loss process arising from, for example, coupling to a normal reservoir or to photoassociation products, the dissipative self-energy replacing the simple constants +/-i gamma and +/-2i gamma in Eq. (A10) would generally become frequency-dependent (non-Markovian), and the jump operator may not remain the bare dot operator d_sigma once the dot is strongly hybridized with the reservoirs. Because the unconventional contribution I_N,uc in Eq. (C3) is built from these self-energies, the sign reversal and the enhancement could be modified or absent under a more microscopic treatment. The authors should either provide a derivation of Eq. (5) valid at gamma/Delta ~ 1 and Gamma/Delta ~ 1, or add an explicit discussion of the model's range of validity and soften the physical claims accordingly. Section IV mentions correlation effects but does not address this Markovian breakdown, which is the load-bearing assumption for the central predictions.
minor comments (6)
  1. [Appendix C (Eqs. C3, C8)] In Eqs. (C3) and (C8), the term beginning with "-1/2 Tr[...]" appears outside the frequency integral even though it contains the Fermi function n(omega); it should be placed inside the integral over omega, or the parentheses should be corrected.
  2. [Eq. (10) and Eq. (C1)] The signs of the right-reservoir terms in Eq. (10) differ from those in the trace in Eq. (C1); the overall minus sign before the integral makes the final current consistent, but the two formulas should be aligned or a sentence should explain the sign convention to avoid confusion.
  3. [Abstract and Section III.A] The abstract states that the current "takes zero at a position in between phi=0 and phi=pi," which suggests a single extra node, while the text also describes multi-node current-phase relations and pi-junction behavior; please clarify which case the abstract refers to.
  4. [Figures 4, 7, 9] The phase diagrams label regions as "anomalous" without stating the quantitative criterion used to distinguish a pi-junction from a multi-node current-phase relation; please define the criterion in the text or caption.
  5. [Throughout] The symbol T is used both for transmission (Eq. 16) and for temperature (Section III), which is a source of confusion; consider using tau or D for transmission.
  6. [Abstract] The name "Gorini-Kossakowski-Sudershan-Lindblad" contains a typo; it should be "Gorini-Kossakowski-Sudarshan-Lindblad."

Circularity Check

0 steps flagged · score 1.0 of 10

No significant circularity: the anomalous currents are computed outputs of the explicitly stated GKSL-Keldysh model, with self-citations that are not load-bearing.

full rationale

The derivation is self-contained within the stated GKSL-Keldysh model. The current formulas (C1)-(C8) are obtained by substituting the explicitly stated Hamiltonian (2)-(4), master equation (5), and uncoupled Green's functions (A8)-(A13) into the Langreth/Keldysh Dyson equations (B1)-(B7); no parameter is fitted to the anomalous zero-crossing, pi-junction, critical-current enhancement, or spin-current reversal. The 'unconventional' contribution I_N,uc in Eq. (C3) is not defined to produce the reversal but is the explicit [g_d^{-1}]^K term that follows from the dissipative part of Eq. (5) via Eq. (A10); its competition with I_N,c is an output. The same holds for I_S,uc, whose conventional counterpart vanishes by the trace identities (C9)-(C10). The main self-citations ([24,37] for Eq. A10 and Eq. (6), [39] for the current expression) are not load-bearing in a circular sense: the dissipative inverse Green's function and current operator are stateable directly from the paper's own Eqs. (5) and (6), and no uniqueness theorem or fitted benchmark is imported. The Section IV caveat about correlations and the inserted skeptic concern about Markovian validity at gamma/Delta ~ 1 are physical-validity limitations, not circularity. Score 1 reflects only the presence of non-load-bearing self-citations.

Assumptions & free parameters 3 free parameters · 6 assumptions · 0 invented entities

The model uses only standard quantum mechanical ingredients: a non-interacting dot, BCS reservoirs, and a Lindblad loss channel. No new particles, forces, or conservation laws are introduced. The free parameters are dimensionless ratios that are scanned to map regimes; none are fitted to experimental data.

free parameters (3)
  • Gamma/Delta (tunneling broadening to superconducting gap ratio) = 0.1, 1, 30 (scanned in phase diagrams)
    Control parameter for the junction regime; not fitted to external data but chosen to explore different limits.
  • T (channel transmission at Fermi energy) = 0.5, 0.1 (scanned)
    Transmission determined by epsilon/Gamma; scanned to map high and low transmission regimes.
  • gamma/Delta (particle loss rate to gap ratio) = 0 to 2 (scanned)
    Dissipation strength; scanned to produce phase diagrams and current-phase curves.
assumptions (6)
  • standard math Keldysh formalism and Dyson equation correctly compute non-equilibrium Green's functions for the GKSL master equation
    The current formulas rely on Langreth rules and Dyson equations, standard tools in non-equilibrium quantum field theory, invoked in Appendices A and B.
  • domain assumption Single-particle loss is Markovian and described by the Lindblad jump operators d_sigma
    Equation (5) postulates the GKSL master equation with loss rates gamma_sigma; this is the standard open-systems description for ultracold atoms and is supported by refs [24,37].
  • domain assumption The reservoirs are described by mean-field BCS theory with a uniform gap Delta
    The uncoupled reservoir Green's function in Eq. (A8) assumes a BCS superfluid; this mean-field treatment is used to compare with cold-atom experiments (refs [17,24]).
  • domain assumption The quantum dot is non-interacting
    H_d in Eq. (4) contains only the on-site energy epsilon and no Coulomb interaction; this simplification is central to the tractable one-particle calculation and is acknowledged as a limitation in Section IV.
  • domain assumption The phase bias is imposed as a gauge phase on the tunneling amplitudes
    The tunneling matrix in Eq. (12) carries phases e^{+- i phi/4}, a standard way to model the Josephson phase difference; the reservoirs are taken to stay in equilibrium.
  • standard math Wide-band limit with constant density of states in the reservoirs
    The parameter W = 1/(pi rho) and the uncoupled Green's functions assume a constant density of states, a standard wide-band approximation used throughout.

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Pith. "Pith review of Anomalous supercurrents in the presence of particle losses." pith.science (2026). https://pith.science/paper/BGZ4YSGM

@misc{pith2026250521085,
  author       = {Pith},
  title        = {Pith review of: Anomalous supercurrents in the presence of particle losses},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/BGZ4YSGM}},
  note         = {Machine review of arXiv:2505.21085}
}
abstract

We show that supercurrent properties in a superfluid or superconducting junction are significantly modified due to single-particle losses present in a conduction channel. In the presence of a spin-independent particle loss, we find regimes where the Josephson current $I_N(\phi)$ takes zero at a position in between $\phi= 0$ and $\phi=\pi$, and the direction of the supercurrent is reversed. Although the region is narrow, we also find a regime in which the critical current is enhanced by dissipation. Such anomalous behaviors in the Josephson current are attributed to a subtle interplay between the contribution that is present regardless of dissipation and the unconventional one that is absent without dissipation. In the presence of a spin-selective particle loss, it is shown that a dissipation-induced spin supercurrent and its reversal occur. The proposed system is analyzed by means of the Keldysh field theory approach based on the Gorini-Kossakowski-Sudershan-Lindblad master equation and may be realized in ultracold atomic gases and solid-state systems.

Figures

Figures reproduced from arXiv: 2505.21085 by the authors.

Figure 1
Figure 1. FIG. 1. Two-terminal Josephson junction system discussed [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. Supercurrent as a function of the relative phase [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. Typical behaviors of [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figures from the paper (5 more)
Figure 5
Figure 5. Figure 5: FIG. 5. Critical current [PITH_FULL_IMAGE:figures/full_fig_p004_5.png]
Figure 4
Figure 4. Figure 4: FIG. 4. Phase diagram of the dissipative supercurrent while [PITH_FULL_IMAGE:figures/full_fig_p004_4.png]
Figure 6
Figure 6. Figure 6: FIG. 6. Particle current in the presence of spin-selective [PITH_FULL_IMAGE:figures/full_fig_p004_6.png]
Figure 7
Figure 7. Figure 7: FIG. 7. Phase diagrams of the particle current at (a) con [PITH_FULL_IMAGE:figures/full_fig_p005_7.png]
Figure 8
Figure 8. Figure 8: FIG. 8. Spin current in the presence of spin-dependent [PITH_FULL_IMAGE:figures/full_fig_p005_8.png]

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    Particle current Figure 6 shows the current-phase relation in different dissipation strengths at (a) Γ/∆≫1 and at (b) Γ/∆≲1. The overall tendencies are similar to those inγ↑ =γ ↓ case 5 in the sense that for Γ/∆≫1 the supercurrent mono- tonically decreases with increasingγwhile the anomalous supercurrent behaviors are obtained for Γ/∆≲1. FIG. 7. Phase dia...

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